Haaland was judged to be onside when Josko Gvardiol played the ball forward, but United were furious over the role of Enzo Fernandez in the build-up.
Fernandez appeared to attempt to head the ball towards goal while in an offside position, although the Premier League Match Centre said the City midfielder had not played the ball and therefore did not interfere with the play.
The decision left Carrick angry as United suffered another disappointing result at home.
"I just don't get it, I really don't get it," Carrick said. "I can't understand how we're trying to help referees, putting so many layers behind them, so many people, bodies and screens, and they can't make the right decision."
The United manager admitted he was disappointed with the result but refused to blame his players for their performance.
"It's worrying if that's how the game's seen by those who are officiating it," Carrick said. "I can't be too critical of the players, and I won't be because I think we've done a lot of good things. Today we didn't quite find what we needed."
The defeat leaves United with just four points from their opening four league matches, increasing the pressure on Carrick to turn their form around.
"I'm feeling for the fans today," he said. "We haven't got as many points as we would've liked at this stage; there's no getting away from that. We've just got to move on and get winning again."
United defender Lisandro Martinez also believed the goal should have been ruled out.
"I think it was offside. What I can't understand is the rules," Martinez said. "He was there. I went to him because he was there in front of me; that's why Haaland was free at the back."
Martinez admitted the defeat was particularly painful because it came in a Manchester derby.
"I want to be calm now; I want to control myself. It's so hard, because you lose, you lose a derby, you lose three points at home ... it's unacceptable," he said.
"Because it's the best league in the world, you have the best teams in the world, the best players in the world, and now we have to go home with this injustice."