The Argentine, who joined Juventus last week, infamously refused to enter the field during a Champions League clash with Bayern Munich in the 2011-12 campaign.
"On TV it looked much worse than it was. When the manager decided to take off Edin Dzeko and introduce a defender, I was upset and sat back down on the bench," Tevez told Tuttosport.
"However, at that moment the really angry one was Dzeko, who started insulting Mancini in Bosnian and the manager replied in Italian. It was a surreal scene.
"I was sitting there talking to [Pablo] Zabaleta and when Mancini turned round he saw me sitting down, but was furious because of the row with Dzeko and took it out on me. My rapport with Mancini wasn't always ideal, but there was always great respect."
Mancini was sacked as the City manager before the end of the 2012-13 season.