Carrick, who has taken charge of United’s last two matches following the sacking of Ole Gunnar Solskjaer, was full of praise for his players as it finished 1-1 at Stamford Bridge.
Keane was furious with Carrick’s comments, and the fact so many of Solskjaer’s backroom staff are still at the club.
The Sky pundit suggested United’s problems are largely down to recruiting people who simply have links to the club.
“Some of the staff have to be held accountable,” Keane said.
“They weren’t just with Ole, they were with Mourinho before that. Are they going to stay on with the new manager?
“I get the impression at Man United the last few years that some of the backroom staff and people upstairs, there’s an element of ‘jobs for the boys’.
“Wink, wink, look after each other, know the right people. That’s why they are eighth in the league.
“We hope it’s not because you know somebody, or you’ve got a certain agent. We hope the right people come in and get the right people for the job. Not because somebody is a decent guy.
“If you want loyalty go and get yourself a dog. You’ve got to get yourself people who are good at their jobs. There’s a bit of a pals act going on at Man United, without a doubt.”
In his post-match interview, Carrick claimed Chelsea were lucky to be awarded a penalty, and also hit back at the criticism United have faced in recent days for their pressing in matches.
Keane felt the 40-year-old was being far too generous in his praise, and that his comments were strange considering his involvement as part of Solskjaer’s team.
“I disagreed with everything [Carrick] said in that interview,” Keane said.
“He’s talking about the penalty, of course it was a penalty.
“He’s talking about being proud of the players’ efforts and being proud of them. He’s been working with the players for the last few months. He was in the dugout with Ole, and now all of a sudden he’s proud of them this week and they had a plan?
“What about all the other games they had? Why aren’t they making an effort the other games? Why aren’t they closing down players in the other games?
“We’ve seen all the stats, they’re the worst in the league at closing people down.
“He’s praising players for doing their jobs. It’s ridiculous.”