Real won the second-leg of their round of 16 tie 2-1 last night, so progressing to the quarterfinal 5-1 on aggregate.
For Alexander-Arnold, the result was signficant after ending on the losing side so many times against City as a Liverpool player.
The Scouser said at the final whistle: "I have lost many titles against City. I know how difficult it was to beat them and we have done a great job.
"Vinicius, (Fede) Valverde, the centre-backs... everyone has worked very well to advance to the next round."
He also said: "I feel the trust that the coach gives me and I can show it on the field of play; I have more confidence. I started the season at a lower level and with several injuries.
"Now I feel very good physically and I think that little by little I bring more things to the team."