Media reports claim Catt told Cipriani that he would "end his England career" hours after the Sale back had learned that he was not in the 31-man squad.
"There are two sides to every story. Everyone knows Mike Catt pretty well," said Lancaster.
"It's a non-story for me."
The Rugby Football Union has admitted that "a robust conversation" took place between the pair, but denied that other players stepped in to defend Cipriani.
Cipriani wrote in the Sun newspaper that he has "a good working relationship" with Catt after the pair spoke the day after the incident, and Lancaster praised the 27-year-old's maturity.
"Danny was excellent, everyone shook hands and it was all done in a short time and we all moved on," he added.
Catt and Cipriani have clashed before.
The 44-year-old coach, who won the World Cup with England as a player in 2003, said in 2009 that he understood why Cipriani's Wasps team-mate Josh Lewsey had punched an "arrogant" Cipriani in their own training-ground confrontation.
Steve Diamond, Cipriani's coach at Sale, believes that England's early exit shows the decision to pick Owen Farrell and George Ford as the only specialist fly-halves in the 31-man squad was a mistake.
"Danny does not need to prove anything to us or his peers. The England coaches are a bit different. That is their decision, rightly or wrongly, and it has proven wrong.
"They pick the best team to get success. He didn't get picked and they did not get success so he will probably feel vindicated."
With England eliminated after defeats by Wales and Australia, Sam Burgess, who has been left out of Saturday's final Pool A game against Uruguay, has played his final match of the tournament.
Lancaster said that he was open to the possibility of moving the league convert from centre to flanker after his Bath coach Mike Ford insisted the 26-year-old would stay at the club and focus on winning his place in the England squad as a blind-side flanker
"Bath used him quite creatively - off six and five-man line-outs stood in the centres as a ball carrier," added Lancaster.
"The more he plays the game, the more I'm sure that they will educate him in the whys and wherefores of lifting and jumping.
"From my point of view, I will have to sit back and see how it unfolds."
England head coach Stuart Lancaster says there are "two sides" to the pre-World Cup training ground row between fly-half Danny Cipriani and attack coach Mike Catt.