But the Gunners are now one win any from winning a third FA Cup in four years and Wenger has been thrilled by his players' response to adversity.
Trailing to Sergio Aguero s second half goal, Arsenal were on the verge of another dispiriting loss in a troubled season after being out-played for long periods.
Sergio Aguero fired City ahead after the break but Nacho Monreal levelled nine minutes later before Alexis Sanchez rescued a woeful performance with a close range victor on 101 minutes.
City has been heavily linked with a move for Sanchez, who is out of contract in mid-2018, in the off-season.
But Wenger was delighted with the way his star kept plugging away until he delivered the killer blow.
However, the lead lasted only ten minutes as Arsene Wenger's team equalised with an exquisite goal when a sublime cross by Oxlade-Chamberlain was volleyed home by Monreal. "In games like that he never gives up".
"It was a very tight game but overall I think we deserved to win the game".
He told BT Sport: "We set out today to get into a final".
"It's a good opportunity to show the Arsenal fans that we can win trophies".
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"We've gone through a very hard period, we faced some adversity that made the situation more hard from inside as well".
"One day I will leave anyway so the most important is Arsenal will always be a great club everyone admires".
He added: "I'm very proud of our performance and the spirit shown".
Guardiola blamed City's wayward finishing for the defeat.
City face a Manchester derby on Thursday but Guardiola was unable to give details on how much football Silva might miss and insisted his team could not have done any more.
"We did absolutely everything to play, like yesterday Tottenham".
"We played like we wanted to and that's all".
"I don't have regrets about the team". "We grew into the game and slowly became better and better".
Sanchez has been strongly linked with a move away from Arsenal with his contract expiring at the end of next season but Wenger insists his match victor is going nowhere.
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