We came here with the objective of trying to win the game but it wasn't enough at the end of the day," Alexander-Arnold told Liverpoolfc.com.
We set ourselves a very tough task after last week, an uphill battle and it was too hard for us to turn around. But, we got the win, a clean sheet as well so there's positives to take. But we know over the two legs we didn't deserve to go through."
He continued: When you are up against it you want to get the early goal and it set the tone of the game when we did that.
I thought in the first half we were really good, boxed them in, kept them in their own half and tried to put as much pressure on them as possible, but they withstood the pressure we put on them.
In the second half we couldn't find our rhythm and didn't create too much and it wasn't enough in the end.
After the game we spoke quite positively about the rest of the season, we've got a month left and we need to give it everything.
That's what we are going to do, we are going to throw everything at it and try to do all that we can. We know it's not in our hands anymore but we need to be as good as possible and just be in the best position that we can to capitalise if teams do slip up."