20 - Arsenal have now reached more FA Cup finals than any other team in the competition's history.
At least they were until Sergio Aguero lifted the ball over Petr Cech to give City the lead on 62 minutes.
Defenders Gabriel and Rob Holding both excelled as part of Arsenal's new look back line and Wenger praised the Brazilian for the way he helped cover for makeshift right wing-back Alex Oxlade-Chamberlain.
Wenger's men went into the extra time after working real hard for the equaliser against a dominating Pep Guardiola side who enjoyed much of the possession throughout the game.
It handed City a first defeat in an FA Cup semi-final in 85 years (eight appearances) with Arsenal also responsible for the last defeat in 1932. "We did absolutely everything to play, like yesterday Tottenham".
Guardiola says he was pleased with the overall performance of his team - and City's FA Cup campaign as a whole - and vowed to make big improvements ahead of next season. "People questioned us, we went through tough times", Wenger said. One day I will leave anyway so the most important [is that] Arsenal will always be a great club that everyone admires.
He said: "We have three or four days to recover [before the game with United]". We looked very strong and unsafe the longer it went on.
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"We went through a hard period". We have some problem to score but we play like we want.
"Today we are sad, but tomorrow we stand up and finish the games we have in the Premier League".
Aguero surged away from Monreal and, although his first touch nearly ruined the chance, he recovered to lift a deft finish over Cech for his 30th goal this season.
"I'm very proud of our performance and the spirit we've shown", he told BT Sport.
"We'll improve next season".
Only Aston Villa's George Ramsay, between 1887 and 1920, can match the six trophies claimed by Wenger, who will be looking to become the single most successful boss in the tournament's history with victory over Chelsea at Wembley Stadium on May 27.
Danny Welbeck couldn't win it for Arsenal with a fine curling strike before extra-time, but Sanchez came to Wenger's rescue with a far more prosaic effort in the 101st minute.
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