The Liverpool teenager fired in a first-half free-kick before a deflected James Milner cross gave the Reds two away goals in their Champions League play-off first leg against Hoffenheim.
But a late Mark Uth strike for the hosts means next week’s second leg at Anfield is still in the balance.
Alexander-Arnold, 18, said: “It’s a thing of dreams to make your European debut for your boyhood club and especially to mark it with a goal.
“We’re disappointed with the late goal but it’s good to take a lead back to Anfield.
“I got egged on to take the free-kick. I had the confidence to finally take it.
“We know it won’t be an easy game but we have strategies to beat them.”
Liverpool skipper Jordan Henderson added: “Trent is brilliant.
“He was outstanding last season and he has come back and gone up a level in pre-season.
“The free-kick is no coincidence he has been doing them every day in training, that is why he is on them.”
Kop boss Jurgen Klopp confirmed he told Alexander-Arnold that he was to take free-kicks after being impressed by the teenager scoring them last season for the club’s Under-23s.
He said: “It was because I told him he has to do it. I don’t want the credit for it.
“He was the only one who could do it. When he played in Under-23 s he took free-kicks and the goal is the same size.”
Klopp also insists he is happy with the result despite Hoffenheim pulling one back late on.
He added: “If you think two and a half hours backwards and someone said we would have won tonight I would have taken each result – even at 8-7.
“I’m happy about the result, yes. I’m not only happy with their goal but I think they deserved the goal over the 90 minutes with their efforts.
“I also thought that we played defensively really well.”
