Carrick, who was in caretaker charge of the club before Ralf Rangnick's appointment, praised his team and their 'pride' after the draw.
However, Keane said on Sky Sports after the game that he 'disagreed with everything he said in the interview' and criticised him for 'praising players for doing their jobs'.
Murphy agreed with 'spot-on' Keane but he did defend Carrick, who was speaking in only his second press conference as a manager.
"I understand the analysis of his post-match words from the Sky pundits and digging him out a little bit, but, to give him a little bit and cut him a bit of slack, he's not used to it," Murphy told talkSPORT.
"It must have been hard for him to come out and be brutally honest in his second-ever press conference as a Manchester United manager."
He added: "Jimmy Floyd-Hasselbaink made a great point, because he is a manager, and he said that sometimes you come out with the emotion still inside you from the game.
"Sometimes you look back on the press conference post-match and you think, 'I got that wrong. Maybe I should have dealt with that differently'.
"I do agree with what Roy Keane is saying. If you can be proud of a group of players for doing their job after months of not doing their job, there's something wrong.
"That's Manchester United football club we're talking about, they've got top-class international players.
"On that point alone, I thought Roy Keane was spot on."
Simon Jordan also agreed and added: "You can have no pride in people doing their jobs. People doing their jobs is a basic fundamental premise, especially for highly-paid, well-rewarded footballers."