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.
There was also debate over City's equaliser, which came from the penalty spot after Cameron Carter-Vickers was adjudged to have fouled Raheem Sterling.
Nine minutes later it was two as former Manchester City youth player Bersant Celina finished off a flowing Swansea move to stun his former employers. "I don't like to lose games when the decisions are wrong but the referees don't want to make wrong decisions, but they must be helped".
"You have to ask the authorities why VAR is not here", City manager Guardiola said.
Ironically Swansea had access to the system in the quarter-finals a year ago - while still in the Premier League.
"It is so hard, because the opponents are so good and we have 10 months with a lot of games".
"We are in the dark ourselves over the non-use of VAR here and that it would only be used in Premier League stadiums", the spokesman told Press Association Sport.
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 are so happy", Silva said.
"We've had a great run and now we've had two defeats".
"I'm here until the summer, we've got loads to play for in the league and the Champions League".
Javi Gracia's side had taken the lead through Etienne Capoue's first-half strike before Michy Batshuayi equalised for Palace after the interval.