The Citizens, who were hoping to take another step in the direction of a double Treble, took Los Blancos all the way at the Etihad Stadium.
Man City and Real Madrid played out a 3-3 draw in the first leg at the Bernabeu, leaving the tie evenly poised for the return encounter.
The visitors broke the deadlock in the 12th minute as Rodrygo took two attempts to fire past returning goalkeeper Ederson.
However, Kevin De Bruyne equalised for Man City in the 76th minute of the match, firing into the roof of the net after a poor Antonio Rudiger clearance.
Neither the hosts nor Real could find a winner in normal time, and extra time didn’t provide any more goals either, so the encounter went to penalty
Rudiger, who made the mistake for Man City’s equaliser, scored the winning spot-kick after Bernardo Silva and Mateo Kovacic had their attempts saved.
The 14-time winners won the shootout 4-3 to progress to the semi-finals at the Citizens’ expense.
Despite Man City losing, there was a lot of respect sent their way by the Real contingent, from defender Nacho, for instance.
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Nacho told Movistar, as transcribed by Sky Sports: “We suffered a lot tonight because City really put you under the cosh. But we are Real Madrid. We always, always fight until the very end.
“We aren’t used to suffering like that. Normally it’s us putting teams under the cosh like that.
“But the only thing which mattered, all night, was making sure it was us in the semi-finals. We showed another side of ourselves; we showed we know how to defend deep and win.”
It’s a shame for Man City that it came down to such fine margins. Nonetheless, they still have two competitions to play for.
Chelsea are up next in the FA Cup, the semi-final taking place at Wembley on Saturday afternoon.
