Haaland converted after Enzo Fernandez, in an offside position, attempted to head Josko Gvardiol's cross but failed to make contact, with Martinez drawn towards Fernandez in the moment the ball broke to the City striker at the back post.
The decision proved pivotal, with United unable to find a way past ten-man City despite Phil Foden's 23rd-minute red card.
"He was there, I went to him because he was there in front of me, so that's why Haaland was free at the back," Martinez told Sky Sports afterwards.
The Argentina international, still visibly frustrated, said the defeat was especially hard to take given the manner of the goal.
"I want to control myself now but it's so hard. It's so hard because you lose. You lose a derby, you lose three points at home."
Martinez questioned the wider standard of officiating in the Premier League, despite acknowledging the league's overall quality.
"Every season, they come to our club and there are discussions about the rules. Then, after, five or six people make this kind of mistake in the Premier League," he said. "I say this 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."
The defender explained the split-second decision he faced in the build-up to the goal, with two City players occupying the box.
"It's difficult because I had two players there and Haaland was behind. I was 50/50 and I had to take the first guy in front. So if he's not there, you go to Haaland. As simple as that.
"But let's see what they want to say now. Let's see. I want to hear what their decision is based on."
Martinez's comments came shortly before the Premier League's refereeing body admitted an "error of judgement" in awarding the goal, acknowledging the VAR should have recommended an on-field review.