The defender, who is in the last year of his contract, was hauled off by manager Arne Slot in the second half.
The club’s vice-captain was seen talking to Slot on the bench, but appeared downcast after his manager went away.
When asked about the incident after the match, Slot said: “I understand every player wants to play 90 minutes.
“But the players on the bench from the start were also not really happy with my choices. We have to take care of him because we need him for the whole season.”
Discussing Alexander-Arnold's role in his team, he added: "He has many, many qualities.
“One of them is crosses from the side, so we can play him in midfield, but I also want him in dangerous positions in and around the goal and in crossing positions.
"He has a lot of freedom to position himself and the rest have to react to it, but it also depends how the opposition lines up and where we can get the best out of him."