Martínez used his post-match interview to question the club’s summer recruitment and single out technical director Jason Wilcox, saying he had expected greater investment to help United compete at the highest level.
Carrick, who was speaking after the defeat in Madrid, said he had heard about the comments but had not watched the interview.
“I need to find out a bit more about it before I can say if and what is going to be done. I really can't comment any further because I haven't seen it,” he said.
The United manager was also asked whether he agreed with Martínez’s suggestion that he had not received sufficient backing during the transfer window. He declined to take a position before seeing the full interview and urged the club to focus on its next fixture.
“I haven't seen the interview; I've heard about it as the interview was done, but I think it's a little bit on the emotions of the game as well,” Carrick said.
“Coming here and being disappointed not to get something from the game. Straight after a game for me isn't the time to talk about that interview because I haven't seen it, so I can't really comment on that.
“But I think it's important for us to move forward quickly, really. There is a big game on Sunday, and it's really important that we move forward and we stay focused on that. There's disappointment within the group. I'm very disappointed in certain things, and the boys are as well.”
United’s defeat followed a difficult start to the season, with the team struggling to turn performances into wins. Carrick nevertheless defended his players’ commitment, saying the disappointment in the dressing room reflected their determination to improve rather than a lack of unity.
“I don't doubt the togetherness or the wanting to win or the willingness to do things to win. I really don't doubt that,” he said.
“I know results-wise, it's easy to look and think there's something kind of deeply wrong because we haven't won enough games, so I understand that.”
Carrick said the squad had continued to work hard despite the results and believed United had created enough opportunities to take something from the match against Atletico Madrid.
“But the players have been great, I have to say. Great not in a nice way, but they want to push, they're willing, they're very disappointed that they haven't come out tonight with something from the game, because we were desperate and we feel actually we could have, and maybe should have.”
Manchester United now have little time to dwell on the defeat, with Carrick keen to ensure the reaction to Martínez’s remarks does not distract the squad from Sunday’s Premier League trip to Leeds United.