Refereeing body Pro Ref later made contact with Manchester United to acknowledge an "error of judgement" relating to Haaland's winning goal.
Haaland turned in Josko Gvardiol's cross at the far post in the 60th minute, with the goal controversially awarded after a VAR check, having initially been disallowed for offside.
The goal proved decisive as 10-man City, who had Foden sent off midway through the first half, triumphed 1-0 at Old Trafford.
In a post on X after the incident, the Premier League Match Centre said the VAR "determined that Haaland was in an onside position" and "deemed that while in an offside position, (Enzo) Fernandez didn't play the ball".
However, Pro Ref said on Sunday evening that the VAR "did not recognise the likely impact" of Fernandez's position and "should have recommended an on-field review".
A Pro Ref spokesperson said: "Following the incident in the 60th minute of Sunday's Premier League fixture between Manchester United and Manchester City at Old Trafford, we can provide clarification regarding Erling Haaland's awarded goal.
"The on-field decision was offside against Erling Haaland – that was checked by VAR and he was found to be in an onside position.
"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."
Old Trafford had witnessed a pulsating 199th meeting of the Manchester rivals on Sunday (Monday AEST) as Enzo Maresca's new-look side won the first clash between the sides since Pep Guardiola's departure.
Much has changed at City this summer but Haaland remains a familiar foe, with the striker's ninth league goal against United taking him clear as top scorer in this fixture in the EPL era.
The visitors had felt aggrieved when Foden was sent off in the 23rd minute for petulantly reacting to a Bruno Fernandes kick, feeling the Portuguese had overreacted.
Marcus Rashford and Kobbie Mainoo hit the woodwork but United could not make the most of their man advantage, with the VAR's decision to then overturn an initial offside call on Haaland's goal causing anger and confusion.
Gianluigi Donnarumma made a crucial stoppage-time save from Bryan Mbeumo to secure a dramatic win that Maresca celebrated by charging towards the City fans at full-time.
Sunday's painful defeat leaves United with just four points from their opening four matches and followed protests about the way the club is being run.
The club's heavy-handed ticket touting investigation has angered fans, who displayed a sign above the tunnel that read "the way you treat us is a disgrace" as Sir Jim Ratcliffe and Avram Glazer watched on.
Earlier on Sunday, newly promoted Coventry's nightmare start to the season continued with a 5-0 home hammering by Brighton which was only exacerbated by having striker Taiwo Awoniyi sent off in the 53rd minute for recklessly elbowing an opponent.
Four straight defeats leave Frank Lampard-managed Coventry rooted to the foot of the standings without a goal and a goal difference of minus 10.
Brighton led 1-0 at halftime through Charalampos Kostoulas before going on a scoring spree after the break with goals from Malick Yalcouye, Pascal Gross, Lewis Dunk and Yasin Ayari.
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