The Reds led 2-0 from last week's semi-final first leg at Anfield, but first-half goals in Spain from Boulaye Dia and Francis Coquelin levelled the tie on aggregate.
A much improved Liverpool regained control in the second half at La Ceramica where goals from Fabinho, Luis Diaz and Sadio Mane gave them a 3-2 win on the night and a 5-2 aggregate victory.
"We never seem to make these Champions League semi-finals easy for ourselves. Difficult, really difficult," Alexander-Arnold told BT Sport.
"We came here and they played very well first half. We regrouped at half-time and got the game by the scruff of the neck. We did what we needed to do."