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.