The Reds were four goals to the good at half time en route to a 7-0 hammering in the reverse fixture a fortnight ago, but they found themselves goalless at the interval on Merseyside following a frustrating opening 45 minutes.
However, Alexander-Arnold provided the cross for Mohamed Salah to open the scoring early in the second half before subsequent goals from Emre Can and Daniel Sturridge sealed the win to leave Liverpool one point clear at the top of Group E.
"We noticed a lot of our chances were coming from crosses so we decided to continue to do that in the second half," he told BT Sport.
"It is hard because their aim is to come here for a point and we want all three. There are different objectives, we want to score and they are trying to stop us. Any team that comes here is always good at that. We have to break it down and we did that in the second half."
Liverpool now only need to beat Spartak Moscow at home on matchday six to guarantee their place in the last 16.