Carrick, who is in caretaker charge of United after the sacking of Ole Gunnar Solskjaer, believed United put in a creditable display to get a draw against the league leaders.
Keane told Sky Sports: "I disagree with everything he said in that interview. Everything he said.
"He's talking about a plan, he's talking about the penalty. Of course it's a penalty. We've all looked at it and it's a penalty.
"He's talking about effort and he's proud of them. He's been working with them for months under Ole. All of a sudden he's proud of them?
"Why aren't they making an effort in the other games? He's praising players for doing their jobs. It's ridiculous."
The Irishman continued: "What about all the other games they had? Why aren't they making the effort in other games? Why aren't they closing players down in other games.
"He's talking about the high pressure it's too much, we've seen all the stats before the match. They're worst in the league closing people down. Winning the ball back.
"Praising players for doing their jobs. He mentioned the three midfielders. He was siting in the dugout for the last few months with Ole. Last few years.
"He was there with Mourinho as well. All of a sudden he's talking about the players this week. He's working with the same players."
Keane added: "I wouldn't be one for getting rid of all the staff but they have to be held accountable, all the staff.
"They weren't just with Ole, they were with Mourinho as well before that, and what are they going to stay on with the new manager? [That's] not necessarily [right], not if they're not up to the job.
"Some of the staff have been here a number of years. I get the impression of Man United in the last few years, whether it be some of the backroom staff or people upstairs, I think there is an element now of a job for the boys now, 'a job for the boys, wink, wink, look after each other, know the right people'.
"That's why they're eighth or ninth in the league."
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