Sanchez pounced on a loose ball to put Arsenal ahead 2-1 in extra time at Wembley, the second time in three years he has decided an FA Cup semifinal in extra time.
Referee Craig Pawson chalked off the strike because his assistant deemed Leroy Sane's cross to the Argentinian to have drifted out of play before reaching the striker.
City's attention now turns to Thursday and a derby which could have a huge bearing on the battle for top-four places in the Premier League.
"I think the referee has to come now and give their point of view as well".
Manchester City manager Pep Guardiola said he was happy with how his team played despite the defeat meaning he would end a season without a trophy for the first time in his coaching career. I am very disappointed.
"I think we have a great team and I hope he's going to be fit but it's going to be hard because a hamstring is always tough to recover [from] quickly".
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Robert Dunham, a former director of the Death Penalty Info Centre, put Arkansas's expiry date consideration into blunt terms. The top photo, provided by the ADC, shows a bottle of Midazolam, with the manufacturer's information blacked out by the ADC.
Serkhio Aguero scored his 30th goal of the season for City in the 63rd minute by racing away to a pass from Yaya Toure.
But they switched off to allow Nacho Monreal to equalise and, despite City hitting the woodwork through Toure and Fernandinho, it was the Gunners who prevailed after Alexis Sanchez scrambled a 101st-minute victor.
We can't see the FA going for that idea because Marouane Fellaini and his unpredictable elbows would have an absolute field day if there wasn't a referee in charge.
Champions League qualification is now essential to prevent the campaign being viewed as a complete failure and the stakes are high for Thursday's clash at the Etihad Stadium. They are going to get confidence and Liverpool, they lost today but it's not finished yet, I think. This league is going to be very tough.
"When you lose in a fair way... there have been a couple of games we have been losing, like against Monaco where Monaco were deserved winners", he said.
"You need to see what is happening behind the scenes, how well the team works and how we operate". What we do we're going to do for him, because it was sad when he was in the dressing room, he wanted to help us.
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