Speaking to reporters traveling with him from Rome, Benedict said the church's top priority now was to help abuse victims heal - yet the comments failed to satisfy victims' groups.
Benedict's historic four-day visit has been overshadowed by disgust over the abuse scandal and indifference in Britain, where Catholics are a minority at 10 percent and endured centuries of bloody persecution and discrimination until the early 1800s.
The trip is the first state visit by a pope to the U.K., and his meeting with Queen Elizabeth II was symbolically significant because of the historic divide between the officially Protestant nation and the Catholic Church.
Yet only 65,000 of the faithful had tickets to an open air Mass at Bellahouston Park in Glasgow, compared to the 100,000 previously expected. The British media has been particularly hostile to the pope's visit, noting its 12-million-pound ($18.7 million) security cost to taxpayers at a time of austerity measures and job losses.
Many in Britain are also strongly opposed to Benedict's hard line against homosexuality, abortion and using condoms to prevent the spread of AIDS. Protests are planned and "Pope Nope" T-shirts have been spotted around London.
Still, a crowd of 125,000 in Edinburgh welcomed him warmly as his Popemobile paraded through the streets, with cheers on Princes Street heard from a mile away and well-wishers waving the Holy See's yellow-and-white flag.
"I've brought my wee girl Laura to see the pope," said James Hegarty, a 42-year-old unemployed Edinburgh resident. "She's only 4, but it's a once in a lifetime chance to see him."
Later Thursday, tens of thousands waved flags and applauded as Benedict arrived in his Popemobile for a late afternoon Mass in Bellahouston Park in Glasgow. At one point, he rolled down the vehicle's window to kiss a baby dressed all in pink.
Scottish singing sensation Susan Boyle warmed up the crowd as she prepared to fulfill a dream and sing before the pope.
The pope's first meeting of the day was with Queen Elizabeth II, both the head of state and head of the Church of England, at The Palace of Holyroodhouse in Edinburgh.
The queen who wore a blue-gray knee-length coat and matching hat and gloves, as tartan-wearing bagpipers marched and thousands of people watched under blustery, cloud-streaked blue skies. The pontiff himself donned a green tartan scarf as he rode through Edinburgh.
The queen told Benedict that his visit reminded all Britons of their common Christian heritage and said she hoped relations between the Anglican Church and the Catholic Church would be deepened as a result.
She also praised the Catholic Church's "special contribution" to helping the poorest and most vulnerable people around the world.
"We know from experience that through committed dialogue, old suspicions can be transcended and a greater mutual trust encouraged," she said. "We hold that freedom to worship is at the core of our tolerant and democratic society."
The pope, too, recalled the shared Christian heritage of Catholics and Anglicans and said he wanted to extend a "hand of friendship" to the British people during his trip.
He said the queen's forefathers' "respect for truth and justice, for mercy and charity come to you from a faith that remains a mighty force for good in your kingdom."
The German-born Benedict's visit also came as the U.K marks the 70th anniversary of the Battle of Britain. Benedict recalled how Britain fought the "Nazi tyranny" during World War II, "that wished to eradicate God from society and denied our common humanity to many, especially the Jews, who were thought unfit to live."
Later, he enjoyed a very Scottish treat: a lunch of haggis - sheep heart, liver and lungs simmered in sheep stomach - at the home of Scottish Cardinal Keith O'Brien.
The queen is head of the Church of England, which split acrimoniously from Rome in the 16th century, a division followed by centuries in which Catholics in Britain were fined, discriminated against and killed for their faith. The visit also coincides with the 450th anniversary of the Reformation in Scotland.
The last papal visit to Britain was by John Paul II in 1982. Benedict's trip is a state visit because he was invited by the monarch.
About 80 people protested the pope's visit, led by a Northern Ireland Protestant leader, the Rev. Ian Paisley, at the Magdalen Chapel where John Knox, the leader of the Scottish Reformation, preached.
"This visit should never had happened. We stand here against these abusers. This is a waste of taxpayers' money," Paisley said.
Benedict acknowledged the opposition in his airborne comments to reporters, saying Britain had a "great history of anti-Catholicism. But it is also a country with a great history of tolerance."
Asked about polls that suggest many Catholics had lost trust in the church as a result of the sex abuse scandals, Benedict said he was shocked and saddened about the scope of the abuse, in part because priests take vows to be Christ's voice upon ordination.
"It's difficult to understand how a man who has said this could then fall into this perversion. It's a great sadness," Benedict said in Italian. "It's also sad that the authority of the church wasn't sufficiently vigilant, and not sufficiently quick or decisive to take necessary measures" to stop it.
He said victims were the church's top priority as it tries to help them heal spiritually and psychologically.
"How can we repair, what can we do to help these people overcome this trauma, find their lives again and find again the trust in the message of Christ?" Benedict said.
He insisted that abusive priests must never again be allowed access to young children, saying they suffer from an illness that "goodwill" cannot cure. In addition, he said, candidates for the priesthood must be better screened.
The Vatican has been reeling for months as thousands of victims around the globe have spoken out about priests who molested children, bishops who covered up for them and Vatican officials who turned a blind eye to the problem for decades. In the latest admission, hundreds of victims have finally come forth in Belgium with tales of horrific abuse that was linked to at least 13 suicides.
Previously, Benedict has admitted that the scandal was borne of "sins within the church" but he had never acknowledged in such detail to the church's failures to act. Advocates for victims have long insisted he take more personal responsibility for the scandal, given that he was in charge of the Vatican office that handled sex abuse cases and was archbishop of Munich when a pedophile priest was assigned pastoral work while undergoing therapy for having abused young boys.
Benedict didn't take individual personal responsibility Thursday, saying only that the "authority of the church" had failed.
The main U.S. victim's group dismissed Benedict's comments as disingenuous, noting that the only real action the Vatican has taken has been to tell bishops to report abuse to police if local laws require them to do so.
"Bishops across the world continue to deliberately choose secrecy and deception over safety and honesty in child sex cases," said Joelle Casteix of the Survivors Network of those Abused by Priests.
Vatican officials haven't confirmed that Benedict will meet with abuse victims while in Britain, but U.K. organizers say arrangements are being made.
A beatification event will follow on Sunday for Cardinal John Newman in Birmingham, which will see the 19th-century English philosopher take a step on his way to sainthood.
The bookish Benedict lacks the charisma of his predecessor John Paul II, who pulled in a crowd of 250,000 for Mass at the same Glasgow park.
The Humanist Society of Scotland placed billboards between Edinburgh and Glasgow that read: "Two million Scots are good without God." It also took exception to the pope's comment Thursday about the Nazis.
"The notion that it was the atheism of Nazis that led to their extremist and hateful views or that somehow fuels intolerance in Britain today is a terrible libel against those who do not believe in God," the group said.
The Rev. Federico Lombardi, the Vatican spokesman, responded that Benedict - who was forced to become part of the Hitler Youth - choses his words wisely. "You can agree or not, but I think the pope knows very well what the Nazi ideology was," Lombardi said.
Associated Press reporter Ben McConville in Edinburgh and Victor L. Simpson and Danica Kirka in London contributed to this report.