Bernardo Silva scored twice in the first half to put City ahead at the Etihad Stadium, before Eder Militao's own goal and substitute Julian Alvarez's added-time strike made it 5-1 to City on aggregate.
However Ancelotti -- whose contract runs until June 2024 -- said the failure to land either trophy shouldn't raise questions over whether he'll still be in charge next season.
"Nobody doubts," Ancelotti said in his post-match news conference, "because the president [Florentino Perez] was quite clear two weeks ago. So nobody doubts."
The Italian coach was referring to remarks that Perez made after Madrid won the Copa del Rey, beating Osasuna 2-1 in the final on May 6, saying "I don't want to hear more about [Ancelotti's future]. He has a contract and we're happy."
Two of Ancelotti's star players, Luka Modric and Vinicius Junior, were also adamant that there was little doubt who would be coaching Madrid next season.
"The boss deserves to carry on, I don't have any doubts," Modric said. "Since he arrived for his second spell he's won every trophy. Last year was an incredible season. This season we did very well in LaLiga until the World Cup, fighting for everything, and then we had some defeats that we didn't want or expect."
Vinicius added: "Of course [Ancelotti] has to carry on. It's a difficult day, but we have to learn lessons from this match so it doesn't happen again next season."
Ancelotti won a LaLiga and Champions League double on his return to Real Madrid for a second spell in 2021-22 -- as well as the Spanish Supercopa -- and has added the Copa del Rey, UEFA Super Cup and Club World Cup this season.
The 4-0 loss to City is Madrid's heaviest Champions League defeat since 2009, when they were beaten by Liverpool by the same scoreline in the round of 16.
"Making an assessment today, in this moment, doesn't make sense," Ancelotti said, when asked to explain the performance. "It's a defeat that hurts, it hurts a lot. But sometimes it can happen in football.
"You get to the Champions League semifinals against a strong opponent, they play better than you and deserve to get to the final. We have to think about next season, the next Champions League, to learn and be better."
"The opponent was better from beginning to end," defender Dani Carvajal said. "We lacked a bit of... I wouldn't say attitude. But we sat back too soon. And when we took a step forward, we had our best minutes."