The Frenchman stopped to make a statement in the mixed zone following the 5-1 win over Cardiff City on Saturday after taking criticism for what some supporters have perceived to be a role in Mourinho's sacking.
Keane, who was speaking to Adrian Chiles on BBC Radio 5 Live, said the behaviour of players made it understandable why Mourinho had a fractious relationship with some members of his squad.
"Jose gave me the chance to play for the best team in the world", he wrote on Twitter.
But by coincidence, his United tenure will start at the ground where his English football managerial career began - the Cardiff City Stadium - and Solskjaer was chomping at the bit to take his place in the dugout. Take risks. I want the players to be the kids that love to play football and go out in front of the best fans in the world. "You would fall out with these players", he said.
"I have so many friends down there and it did not turn out a success with results but I learned a lot, the club learned a lot, everyone is happy today anyway (for being back in the Premier League)". That's my comeback to players, you might come on make an impact.
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The former Manchester United captain directed a tirade at the Old Trafford stars after the Portuguese boss was sacked on Tuesday before being replaced with interim boss Ole Gunnar Solsjkaer. "We are in December and we will try and recover and try and win games again", shrugged Guardiola, conceding that his side needed to "recover mentally and recover physicality". We can not play like this and score five goals and then lose.
"I'm sure all the players are now looking to the next game, the points, and we have to go back into and we want to go back to the top of the league". It's not just at United, the modern players are very weak, you can't say a word to them.
Mourinho fell on his sword earlier this week after steering Manchester United to their worst start to a season in living memory, with the Red Devils already 19 points behind league leaders Liverpool after just 17 Premier League games. "They are a great bunch of players and their quality is unbelievable".
"He's been well received, he's well liked, but I really think he'd be the least person I think of out of all of us to become a manager", Yorke added.