Price accused Hallion of directing a profanity toward him during the Rays' 8-3 win over the White Sox on Sunday. The AL Cy Young Award winner thought Hallion missed a pitch and exchanged words with the plate umpire while heading to the dugout after the seventh inning.
After the game, Hallion vehemently denied Price's claim.
"I'll come right out bluntly and say he's a liar," he told a pool reporter.
Price took to Twitter to dispute Hallion's version of events and said before Tuesday night's game in Kansas City that he was upset with himself and never looked up until he heard Hallion's voice.
"You can't talk to me that way, period," Price said. "That was my whole thing. It had nothing to do with the strike zone. You don't talk to people that way."
Price also took umbrage with being called a liar.
"I'm not a liar," he said pointedly. "I'm not a liar, period."
Two of Price's teammates, pitchers Matt Moore and Jeremy Hellickson, came to Price's defense from the dugout during the game. Hallion ejected Hellickson after he warned them to keep quiet.
Moore and Hellickson joined Price in addressing the issue on Twitter, with Hellickson saying, "There's only one person lying about all this and his name starts with a T and rhymes with pom.
Price and his teammates could be disciplined for violating MLB's social media policy, which forbids "content that questions the impartiality of or otherwise denigrates a Major League umpire."
Hallion also could be disciplined for initiating the incident.
Asked if it would be awkward the next time Hallion umpired one of his games, Price replied: "Not for me."
Earlier Tuesday, Price stopped by the Negro Leagues Baseball Museum in Kansas City, where he was presented with the Wilber "Bullet" Rogan Award as the American League's top pitcher.
A three-time All-Star, Price went 20-5 with a league-leading 2.56 ERA last season. He finished tied with the Los Angeles Angels' Jered Weaver for the most wins in the majors.
"It's heavy," Price said with a smile, hefting up the trophy while sitting in the visiting clubhouse at Kauffman Stadium. "I like it when they're heavy."