Haaland's strike on the hour mark was initially disallowed for offside but was allowed to stand after a VAR review found him to be onside.
However, Pro Ref said the VAR failed to recognise the likely impact of his teammate Enzo Fernandez, who attempted to head the ball from an offside position.
"The on-field decision was offside against Erling Haaland - that was checked by VAR, and he was found to be in an onside position," the statement said.
"In the same attack, it was established that Enzo Fernandez did not play the ball and therefore that makes any offside offence subjective; however, on this occasion, the VAR did not recognise the likely impact of his position and should have recommended an on-field review.
"Contact has been made with Manchester United this evening to acknowledge what we deem is an error of judgement. A review of the incident will take place."
Manchester United boss Michael Carrick was angry at the decision as his side slumped to a derby defeat.
"I just don't get it, I really don't get it, 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," he told a post-match media conference.