The Reds defeated Southampton 3-1 at Anfield, but not before Saints held a 1-0 lead.
Alexander-Arnold told LFC-TV: "Probably the most (angry) we have seen him so far, I guess it's a good thing he's not been too animated so far, but I think rightfully so.
"It wasn't good enough, we deserved to be down, but we came out second half with a point to prove and did that really early on. As a team and individuals, you'd like to be very good every single game but it's not possible.
"You are going to have days like this where you don't play well, you're not proud of the performance. It's a day you look back on it and think yeah we got the three points, that's the most important thing."
The fullback also said: "You can't downplay too much how important today's win was, to go 16 clear at this stage of the season is huge and puts a lot of pressure on Arsenal.
"We've done our work in the league now until after the internationals, now we focus on the two other competitions."