The United boss was already under pressure as the Red Devils headed to Madrid, where they failed to secure a result despite the expensive new-look midfield trio of Carlos Baleba, Andrey Santos and Youri Tielemans all starting.
Speaking at full-time, Carrick said he had mixed feelings after what he felt was an encouraging showing: "Bit mixed. It is a tough enough place to come and to get the start we had obviously puts us in a difficult situation but I thought we grew into the game.
"We started having some control in the second half without having real threat. Then there was Bruno's chance and then the red card, which I felt was a poor decision.
"Disappointed really with the chances that we had, and that we hadn't had more.
The mood seems low in the Man Utd camp
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"We tried something a little different. I thought in possession and playing through the pitch was good at times. Defensively, we probably let them switch the play too much, which put us on the back foot at times.
“In the main, we dealt with that and Senne (Lammens) didn’t have too much to do. We feel the game was there for us, is the biggest thing, so we could and should have got more from it.”
With pressure mounting, Carrick was asked how soon he expects his side to click and rediscover the fine form on which they finished last season.
“We need to find a way, for sure. Today was a one-off game. It's the Champions League here, it’s a tough place to come. In that sense, the bigger picture is a different story. We need to improve certain things, we are doing certain things OK, but we need to win games, for sure.”
Asked to respond, Carrick said he had not yet seen Martinez’s comments, but called for his squad to stick together through a chastening period.
"We all care and show that in different ways but now is certainly the time to be together and work through. We have a big game on Sunday now and we need to prepare for that."