Matt Grimes opened the scoring for the Championship side after converting from the spot kick.
City finished the tie off with goals from Bernardo Silva and Aguero either side of a Kristoffer Nordfelt own goal - the Swansea goalkeeper unfortunate that Aguero's penalty attempt hit the post only to hit the back of him and go in.
It was a lucky escape for City as replays showed Raheem Sterling was fortunate to win the penalty that led to the equaliser, while Aguero was marginally offside for the victor.
United were under increasing pressure in the second half as Wolves continued probing, with Raul Jimenez's header pushed over the top of the crossbar by Romero on 55 minutes.
'We deserved to win the game by far - but to win in that way, I'm sorry'.
"They ask all the clubs about the VAR (video assistant referee) and all around Europe the VAR is there and here it's not".
The Premier League side struggled to break Swansea down after the break, but Bernardo Silva's goal in the 68th minute got the visitors back in the match.
Having already won the League Cup and advanced to the Champions League quarter-finals, City remain in the hunt for an unprecedented clean sweep of all four major trophies.
"That's important because for the future, for the new players and managers who are coming, they will learn from this group of players, and this group of people, that we never give up and fight for every single game and title until the end".
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Guardiola was less impressed with the Swansea fans, who invaded the pitch following the final whistle with substitute Oleksandr Zinchenko appearing to be jostled by one supporter. "It's not nice but thankfully nothing happened", he said.
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