Bernardo Silva and Mateo Kovacic missed from the spot as holders City were beaten 4-3 on penalties after a pulsating quarter-final tie ended 4-4 on aggregate.

City's defeat means there will be no English club in the last four, after Arsenal were earlier knocked out by Bayern Munich.

The German champions won 1-0 in Munich to clinch a 3-2 aggregate victory.

Rodrygo gave Real an early lead in the second leg at the Etihad Stadium but City otherwise dominated and, after creating a host of chances, finally made it 1-1 on the night through Kevin De Bruyne in the 76th minute.

De Bruyne spurned a good chance to win the tie in normal time but it was the competition's record 14-time winners who ultimately prevailed.

Ederson lifted City by saving from Luka Modric in the shootout, but Andriy Lunin denied Silva and Kovacic to send Real through.

"We dominated the game, the whole game," City defender Ruben Dias said.

"Until the penalties, the effort was there. We had our chances ... it's difficult to take."

Outstanding Madrid midfielder Jude Bellingham said he was "pretty much dead on my feet" after an all-action display.

"To win the game is a massive reward," he said.

"Most teams would fall apart when City get on top, the crowd gets going, but we stood up really well for another half-an-hour, 45 minutes, and worked hard."

Madrid will face Bayern Munich in the semi-finals after Joshua Kimmich's bullet header was enough to send the German giants through.

Borussia Dortmund will take on Paris Saint-Germain in the other last-four clash.

Bayern showed the sort of pedigree in the competition that comes from years of being involved in the business end of the tournament - they have now qualified for 13 semi-finals and have reached the stage nine times since Arsenal's last semi-final appearance in 2009.

"It was a chess game in the first half," Bayern's Thomas Tuchel said after becoming only the second coach to guide three different clubs to the competition's final four.

He also led Chelsea and PSG to the semi-finals.

"Nobody wanted to make the first mistake. Everyone played a bit safe - there were moments for us, there were moments for Arsenal.

"We encouraged the team at halftime to show a bit more personality, a bit more courage."

Having lost 2-0 at home to Aston Villa on Sunday to dent their Premier League title hopes, Arsenal's European exploits came to a shuddering halt as Bayern's nous took them into the last four.

"What we still have to play for is beautiful," disappointed Gunners manager Mikel Arteta said, looking forward to the EPL run in.

"It's easy to ... praise the players and talk nice things when we win 10 in a row and one draw.

"The moment is now to be behind them and be next to them."

Australian Associated Press