Federico Valverde netted a first-half hat-trick for Madrid to secure an impressive last-16 first-leg victory.
Alvaro Arbeloa's side have been inconsistent over the past few weeks but delivered their best display of the season at the Santiago Bernabeu.
"(It was a) massive performance, I think a lot of the noise when the draw happened and then leading up to this game," Alexander-Arnold told TNT Sports.
"Especially (given) the way that we've been playing the last few games, and the results we've had, a lot of people just expected us to get battered tonight.
"It just shows the mentality, it doesn't matter what injuries you've got, what players out, this competition means a lot to the club."
Madrid were without key players including Kylian Mbappe, Jude Bellingham and Rodrygo Goes among others, but Valverde's treble secured the record 15-time winners a convincing victory.
"I'm very happy for Valverde," Arbeloa told reporters after the victory.
"I think he is the Juanito of the 21st century... he is a perfect representation of Real Madrid."
Juanito, a Madrid icon in the 1980s, was known for his fighting spirit and character.