Liverpool continued exactly as they left off last term by stuffing newly-promoted Norwich 4-1 at Anfield.
First-half strikes from Mohamed Salah, Virgil van Dijk, Divock Origi and an own goal guided the Reds to an opening-day win.
After winning the Champions League and finishing one point behind Premier League winners Manchester City last season, expectations are high on the red side of Merseyside.
But Alexander-Arnold wants to put to bed the success of last term and focus on what is in front of him.
“I think for us now the celebrations are over,” he said.
“We have to focus on the new season. it is about putting it past us.
“We did a special thing last season but it’s a new season and that doesn’t matter now.
“We can look back at thee and of our careers but we need to focus on going one better in the league and obviously getting as far as we can in all the other competitions we’re in.”
Alexander-Arnold registered two assists as Liverpool rose to the top of the Premier League table.
And he is excited to compete against fellow full-back Andrew Robinson during the remaining 37 matches.
“I think we need to keep the same output and create as much for the team as we can,” Alexander-Arnold added.
“The way that we play as full-backs in this team is getting up and defending as well.
“No matter what you can always improve. Of course we want to keep more clean sheets than we did last season.
“We can still get better and the output at the other end.”