The Arsenal boss took exception to Mourinho's "boring" jibe, while the Man City coach was on the defensive over a comment about FFP.
Arsene Wenger and Manuel Pellegrini have accused Jose Mourinho of showing them a lack of respect.
The Chelsea boss called Arsenal chief Wenger’s failure to win the title since 2004 ‘boring’.
But the Frenchman hit back yesterday, saying: “The biggest thing for a manager is to respect each other and some people have to improve on that.
“Everybody lives with his own internal problems and I live with mine. That is enough.”
Mourinho, poised to claim the Premier League title from Manchester City on Sunday, also claimed that Pellegrini’s club should have been docked points rather than fined for their failure to meet Financial Fair Play regulations.
Pellegrini said: “Every manager can say what he wants about Financial Fair Play rules.
“We didn’t lose points because we didn’t deserve to.
“There are so many things he always says that don’t matter, about Chelsea or referees or the FA Cup or other managers or other things.”
Pellegrini had several clashes with Mourinho while they coached in Italy at rival clubs and the Chilean does not agree with his win-at-all-cost attitude .
He added: “When you think everything is normal to say to win, you can say what you want.”
Wenger also confirmed Chile star Alexis Sanchez could miss the start of next season due to this summer’s Copa America, which starts on June 11, in his home country.
But the winger will be available for the FA Cup Final against Aston Villa May 30 after Arsenal struck a deal with Chile.
Wenger said: “If Chile go very far he will miss the start of the season. They could call him up but we got an agreement that they won’t call him up.”