Alexis Sanchez scored in extra-time to secure a 2-1 win at Wembley and send the Gunners into the final for the third time in four years.

It gives Arsenal and Wenger a chance to salvage a disappointing season and could ease some of the pressure on the manager, who said it proved his side could still compete with the top teams despite a string of recent Premier League losses.

"I felt it was a big mental test for us today because many people questioned that, can we turn up on an occasion like that?" Wenger said.

"That's why I'm very proud of the players. As a manager, your biggest joy is when you feel you have a real team performance. That was the case today, and that's why I'm happy today."

Wenger, who has yet to announce whether he will sign a new contract this summer, said he did not want to look at the win as a personal vindication.

"Honestly, when you watch the stands today and you see how big this club is, I just feel happy when our fans go home tonight and are happy," he added.

"And when I don't win the games I feel sad because I don't feel that I give what people want.

"We have gone through a very difficult period, and we have faced some adversity that made the situation even more difficult from the inside as well.

"But we have shown a united response, not a divided response. But of course, mentally we were in a fragile position."

Arsene Wenger celebrates Arsenal's FA Cup semifinal win on Sunday.

Wenger won the tactical battle against Pep Guardiola, sticking to the back-three formation he had deployed against Middlesbrough last Monday.

It meant City were allowed to dominate possession, but Arsenal's defence -- which has looked so fragile in recent months -- held firm until Sergio Aguero was able to outpace Nacho Monreal and chip past Petr Cech for the opening goal.

However, Monreal levelled 10 minutes later, thumping home a cross from Alex Oxlade-Chamberlain, and Sanchez pounced on a loose ball to net the winner in the 101st minute.

Arsenal's three centre-backs -- Laurent Koscielny, Gabriel Paulista and Rob Holding -- dealt well with City's dangerous attackers throughout the game.

Gabriel had one of his best games in an Arsenal shirt, and Wenger said: "Today I felt he could intervene for Oxlade-Chamberlain on [Leroy] Sane's ball through. Sane goes a lot in behind, and I felt he had the pace to cover and to tackle, and he did that very well.

"In the second half I think he saved three, four balls. So I just thought he is well-suited for this position."

The new defensive formation has brought two straight wins, but when asked if he should have made the switch sooner Wenger said: "I like your question, because it shows exactly what our job is.

"No matter what you do, even if you get it right at some stage, people say: 'Why didn't you do it earlier?'

"The opposite is right as well. If you get your starting lineup wrong and you change it half-time, people say: 'You see, he's a tactical magician because he changed the team at half-time.' But they forget that he got it wrong at the start.

"I think what I did was just to give a bit more security to a team who conceded three goals in the last three away games."