But Price evidently was, at the very least, annoyed by Ortiz's declaration of "war" against him.
"He was mad, so I get it," Price told reporters Saturday, referring to Ortiz's postgame comments Friday. "We all say stupid stuff when we're mad. [I have] been there. I'm sure he probably wishes he wouldn't have said some of the things he said. You can't relate the game that we play to a war.
"Kellen Winslow got a lot of crap for saying he was a soldier. You're not a soldier. This is not war. We have troops fighting for us that are in a war. It's not a good comparison."
Ortiz was outraged Friday after Price drilled him with a first-pitch 94 mph fastball, setting the tone for a game that featured another benches-clearing incident between the AL East rivals. Ortiz, who homered twice off Price in last year's ALDS, said he had lost all respect for the former Cy Young Award winner after Boston's walk-off victory.
"I mean, it's a war," Ortiz said. "It's on. Next time he hits me, he better bring the gloves. I have no respect for him no more."
Price chose not to address Ortiz's comments Friday night but was much more talkative Saturday.
"For as many people as I quote-unquote 'lost respect from,' I gained respect from a lot more people," Price said. "And I know that's a fact."
Price, who also hit Mike Carp with a pitch Friday, insisted after the game that he was simply trying to establish the inside corner against Boston's left-handed bats. But Price suggested otherwise a day later, taking issue with Ortiz's habit of admiring his home runs.
"Sometimes, the way [Ortiz] acts out there, he kind of looks like he's bigger than the game," Price said. "That's not the way it is, not the way it goes. ... Nobody's bigger than the game of baseball. You ask pitchers from 10, 15, 20 years ago -- that's normal, part of the game."
Price also said he does not plan on talking with Ortiz to settle their differences.
"We've got nothing to talk about," he said.
The Red Sox beat the Rays, 7-1, on Saturday for their sixth straight victory. The teams complete a three-game series at Fenway Park on Sunday and will not play again until July 25 at Tropicana Field.
ESPNBoston.com's Gordon Edes and The Associated Press contributed to this report.