United were beaten 1-0 at Old Trafford despite playing the majority of the match with a numerical advantage, after Erling Haaland's goal was awarded following a lengthy VAR review.
Speaking to BBC Radio 5 Live, Carrick admitted his side's overall performance was mixed, but reserved his strongest comments for the officiating around Manchester City's winner.
"It was a mixed performance. I think we were in good shape for a lot of the game and started the second half better than we ended the first half," Carrick said. "It looked like something was about to happen and then they scored their goal.
"I don't really know where to start with that goal to be honest, but that was a major part of how the game panned out in the end. For a decision to go like that against us is tough to take, I have to say."
Manchester United struggled to make the most of their numerical advantage after Phil Foden's first-half red card, according to the head coach.
"It changes some of the details. We didn't probably get to grips with that well enough in the first half. You have to adapt and adjust. It put us in a good place that we didn't get the most out of."
Carrick reserved his sharpest criticism for the wider application of VAR, rather than any individual official.
"I've got a big concern if I'm honest because I think we put so many layers behind referees now, screens, more bodies, more offices to get decisions right, and the dangerous bit for me is how the rules are being interpreted," Carrick said. "I'm really concerned about how the game is seen from that angle. He has thrown himself with a full diving header. From one angle you are thinking if he has touched it or not. Martinez has to react to that, it has a major impact on the whole action. The line itself I wasn't convinced it was drawn in a great position. I'm staggered and a little bit worried and concerned that if that's how it's interpreted we are in a bit of bother."
Despite the defeat, which leaves United with four points from four Premier League matches, Carrick insisted he remains confident in the direction of the team.
"We will get there, I'm convinced of that. We haven't got as many points as we wanted and we should have. We've got to accept that and take that. There have been a couple of reasons for that and that's it. It doesn't change us moving forward and our hopes for the season and what we can achieve as a team. We've made really good strides over a period of time and we will continue to do that."