Instead, the Parkers said they and Peter Lanza shared their condolences for one another and talked about his son, Adam Lanza, during the emotional meeting, which lasted more than an hour.
"I don't feel like he should be held responsible for what happened that day," Allisa Parker told "CBS This Morning," during the second part of an interview that aired Friday. "That was not ultimately his decision to do that, so how can I hold him responsible? Were there missteps in the raising of his son? Possibly."
Adam Lanza, 20, fatally shot 20 children and six educators with a military-style rifle on Dec. 14, then killed himself as police arrived. Authorities say he also killed his mother at their Newtown home before he went to the school. The Parkers lost their 6-year-old daughter, Emilie, in the rampage.
Allissa Parker said she told Peter Lanza that there was an opportunity to learn from the killings and his cooperation was vital.
The Parkers wouldn't reveal what Peter Lanza said about his son. Connecticut state police haven't released any information about a motive, but people close to the investigation have told The Associated Press that Adam Lanza showed interest in other mass killings and had literature on other mass shootings at his home. The people spoke on conditional of anonymity because the investigation is continuing.
Peter Lanza, who was divorced from Nancy Lanza, has declined to comment about the meeting with the Parkers, who said they came away from it with a better understanding of Adam Lanza.
Robbie Parker, who was among the first of the victims' parents to publicly discuss the shooting, said he and his wife wanted to meet with Peter Lanza because he was the only person who could answer their questions.
"Adam's gone and his mother's gone, and those are the two people that could give us the most information to the questions that all of us have," he said.
The Parkers, who have two other daughters ages 3 and 5, said they're not angry because they know they can't undo what happened at the school that day.
"So the idea of wasting any energy on anger towards somebody or trying to point blame at anybody seems like a waste of time and energy that we can use to be better parents to our girls," Robbie Parker said.
Allisa Parker said she believes Nancy Lanza bears some accountability for what happened. The Bushmaster rifle used in the school shootings belonged to Nancy Lanza.
Asked whether she forgives Adam Lanza, Allisa Parker said it's not her burden to bear.
"I do hold him accountable, but I feel like God will determine that," she said. "And I feel like he's in a place where the judgment will happen, and I don't have to. I don't have to judge him, and I'm at peace with that."