The 15-time winners are 24th in the 36-team table with three games of the league phase remaining and run the risk of failing to make the knockout stages.
Liverpool, by contrast, are flying at the top of the table with a maximum 15 points from their five games and are also eight points clear at the summit of the Premier League.
"From the first minute they just took control of the game," Bellingham told TNT Sports on a disappointing return to England.
"I just think they were more up for it than us, to be honest, which is really disappointing to say.
"It's a bad result against probably the best-performing team in Europe. It's no disgrace to come here and lose, but we are disappointed in how we performed.
"The important thing is we use it the right way now. We've got three games left in the group and it's important that we go and try and win all of them to give ourselves the best possible chance in the standings."
Mbappe miss
Thibaut Courtois frustrated the Reds in a dominant first half from the hosts, just like he did in Madrid's 1-0 Champions League final win between the sides in 2022.
Alexis Mac Allister finally made Liverpool's pressure count early in the second period.
But Madrid had the chance to level when Kylian Mbappe's penalty was saved by Caoimhin Kelleher.
Arne Slot oversaw Liverpool's first victory over Real Madrid in nine meetings
Arne Slot oversaw Liverpool's first victory over Real Madrid in nine meetings © Oli SCARFF / AFP
Mohamed Salah also fired wide from the penalty spot for Liverpool, before Cody Gakpo's header secured the three points.
"He's a wonderful player but the pressure that he holds, because of how good he is, is huge," added Bellingham on Mbappe, who has failed to shine since his much-anticipated move to the Spanish capital.
"The penalty is not the reason why we lost the game. As a collective, we weren't good enough on the night. They performed better than us and it's as simple as that.
"Kylian can keep his head high. I know for sure that he will produce many more moments that are huge for this club."
Victory ended Liverpool's eight-game winless run against Madrid, that also included defeat in another Champions League final in 2018.
"You know how special it is to play against a club that won this Champions League so many times, are the reigning champions and were a pain in the ass for Liverpool many times as well," said Liverpool boss Arne Slot.
Kelleher's penalty heroics continued his fine form since stepping in to deputise for the injured Alisson Becker.
"In most situations you think it's probably gonna go in because they have such a great record but both (Mbappe and Salah) missed so they showed us today that they are human beings," added Slot, who has won 17 of his first 19 games since replacing Jurgen Klopp.
"In Mbappe's situation Kelleher saved it which made it even more special for us. I don't think there was a situation where he was not outstanding for us."
© 2024 AFP