LONDON, England -- Even tired and disappointed, Manchester City can still find a way to win.

After their Champions League exit to Real Madrid on Wednesday, following 120 minutes and a penalty shootout, City turned up at Wembley three days later for an FA Cup semifinal on Saturday against a Chelsea side fresh and in form.

Man City manager Pep Guardiola was furious that his team were asked to play in the Saturday semifinal instead of getting an extra day's rest and playing on Sunday, but where lesser teams would have crumbled, City still found enough to win 1-0 and book a Wembley return for the final at the end of May.

It was nowhere near a vintage Guardiola performance, but he won't care. City's character and resilience was best summed up by Bernardo Silva, who scored the winner after missing a crucial penalty against Real Madrid.

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Silva is a softly-spoken, mild-mannered type of footballer and his miss in the shootout against Madrid will have hurt him perhaps more than it would have done others. His goal in the 84th minute on Saturday was enough to see off Chelsea and, after being congratulated by his teammates he turned alone to the City fans behind the goal to beat the badge on his chest. Few of his other 66 goals in a blue shirt will have meant more.

Chelsea had so many chances to score that Guardiola spent most of the game crouched down with his head in his hands, but by the end was left celebrating what he insisted was one of the best performances of his eight years in charge.

"What they have done today is one of the greatest things I have seen from a group of players," said Guardiola. "In terms of quality football and mistakes, it was not [good] but absolutely [it was one of his best performances]. In these conditions, travelling to play against Chelsea in their best moment of the season and done what we have done today? I don't know how we survived.

"I said to them, 'Don't fight against your feelings.' If you're sad and disappointed it's fine," he added of immediately playing the FA Cup semifinal after their Champions League exit. "Don't pretend to be happy all the time in life. I said to them 'I'm sad. But once you're here, do your best.' And they did it."

After eight minutes of stoppage time, Guardiola raced onto the pitch to embrace his players while Chelsea manager Mauricio Pochettino trudged off the Wembley pitch for a second time this season with a feeling of what might have been.

Pochettino's future as Chelsea manager is set to be reviewed at the end of a season during which he was expected to achieve more than bounce around in mid-table. And if it turns out he needed to win the FA Cup to keep his job, it's unlikely Nicolas Jackson will be at the top of his Christmas card list.

Before Silva's intervention, the 22-year-old Jackson had three golden chances to put Chelsea in front and each one was fluffed. In the first half he was sent clear, rounded Stefan Ortega, and inexplicably stopped. Then, in the second half, he got inside Kyle Walker and with a clear sight of goal saw his shot saved by Ortega. Moments later, Cole Palmer clipped a ball to the back post and Jackson's weak header was beaten away by City's goalkeeper.

As Jackson missed chance after chance, Pochettino watched on from the touchline with his arms out-stretched, seemingly disbelief. At the final whistle, Silva punched the air and ran towards the City fans while Jackson slumped to the floor and sat, motionless, for a few minutes.

Chelsea had more shots on target than City (five to three) but where Silva was clinical with their one clear chance, Chelsea were wasteful and then some. Midway through the second half, Moises Caicedo raced through and, with Jackson unmarked in the centre, managed to punt his cross into the stands. And as if to sum up their entire afternoon, while they chased a late equaliser, Ben Chilwell escaped down the left and twice decided not to cross to Raheem Sterling before seeing a half-hearted cross easily intercepted by Ruben Dias.

Only Jurgen Klopp and Jose Mourinho have won more matches against Guardiola than Pochettino and, although he got a lot of his tactical plan right, the finishing touch for Chelsea was always missing.

"I think in the game we were a little bit better and deserved more, but it is not about deserving it, it is about being clinical and we were not today," said Pochettino, who also said he thought Chelsea should have had a penalty when Palmer's free-kick hit Jack Grealish's hand.

"I think last Monday [against Everton] we scored six but today we were not capable of scoring even with having maybe more chances and more clear chances to score," Pochettino added. "We were not capable of being clinical in front of goal, we had many chances but we did not score."

On the balance of the chances they created, Chelsea should have won the Carabao Cup final here in February and they should have beaten Manchester City. But instead, Chelsea lacked the necessary polish, so Liverpool went home with the Carabao Cup and City are into the FA Cup final.

While Chelsea are left trying to salvage something from their season by trying to scrape into the Europa League or Europa Conference League, City can still end the campaign as the first English team to win back-to-back league and cup doubles.

For all the praise and plaudits, Guardiola's football receives, it's the character and spirit of his players that he values the most. It was on show again against Chelsea and City -- favourites for the Premier League and into the FA Cup final -- have earned another chance to make history.