Pep Guardiola's men won the tight encounter 1-0 but the Toffees were fuming after having a late handball shout turned down by match officials despite clear contract from City star Rodri.
Everton took their complaint to the the PGMOL (Professional Game Match Officials Board) and were subsequently given an apology by the Premier League upon request.
It's understood that Everton's chief executive, Denise Barrett-Baxendale, wrote to the league after the weekend's fixture highlighting the incident and demanding an apology.
However, whilst the former Charlton Athletic and Ipswich Town players agree the officials' decision making for the handball was 'poor', they both said league bosses were wrong to say sorry to Merseyside club, saying it sets a bad precedent.
When asked by talkSPORT Breakfast presenter Laura Woods whether it was the right decision for the Premier League to apologise, Bent stood firm on his thoughts on the issue.
"No, because it's part of football," he said. "It's a decision. It's a bad decision I understand that, but you set the precedents by apologising.
"You look what's happened throughout the last couple of seasons, look at Aston Villa with the goal line technology. Teams got relegated because of it and that point effectively kept them up.
"These things happen and it's unfortunate that it happened to Everton, they've should've had a penalty. Someone made a mistake, but you've got to just live and die by your decision, move on to the next.
"The moment you start apologising for this, apologising for that, you set a real precedent so, no, I think it's poor that they came out and did that".
Later on, Ambrose joined Alex Crook and Sam Matterface on the White and Jordan show and labelled Everton's demand for an apology 'cringe', despite them deserving to have the incorrect call recognised.
"It was an absolutely outrageous decision, of course, and they should have got a penalty," he said. "It was handball, everyone knew it.
"The Manchester City players knew it, Rodri knew it, so that's obviously been discussed.
"I think it's a little bit cringe Everton asking for an apology, in an honesty. You can place that [the wrong decision] on record without asking for an apology and I think it's even worse that they've been given an apology."
Referees' chief Mike Riley sent a direct apology to Toffees boss Frank Lampard following the club's complaint and this is a decision that Ambrose believes has set a bad standard in the game going forward.
"You're opening a can of worms here," he explained, "Everyone who has a bad decision [go against them], are they now going to be expecting an apology?
"I think there have been bad decisions from VAR, but what does this apology achieve?"