ReactionTrent Alexander-Arnold: It doesn't matter how, we got the job done
Sadio Mane's finish in the 27th minute at Anfield was enough to secure the three points for the Reds in the Premier League contest.
While Alexander-Arnold produced the assist for the game's only goal, the full-back took more satisfaction in the clean sheet he and his teammates earned.
The No.66 told Sky Sports: "We tried to get forward when we had the chance and I think we created some chances.
"But always our aim, first and foremost, is to keep a clean sheet, make sure we win the game. I think we've done that very well.
"We've been able to keep a lot of clean sheets over the last few weeks especially and we're looking to keep that up and make sure we carry on doing that for the rest of the season."
On Liverpool being able to grind out results, he continued: "We've been able to do that recently. You look at the Burnley game – we've been able to go there and get a 1-0 win.
"We've been picking them up over the course of the season. These are the ones that really matter.
"It's always nice winning 4-0 or 5-0, but it's three points at the end of the day – it doesn't matter how you do it, just get the job done. We've been able to do that again today."
Not long before half-time, Alexander-Arnold was on hand to produce a heroic goalline clearance to keep out Pablo Fornals' chip over Alisson Becker.
The Scouser chased down the finish in the nick of time, despite initially believing the West Ham attacker had been offside.
He said: "I thought it was offside, personally, but I was wrong.
"I saw it back at half-time and I was wrong, but you play to the whistle these days, that's the main message we've been told.
"So I've done that and been able to clear off the line and keep the clean sheet."
ReactionArne Slot press conference: Southampton win, 'special' Salah and not getting carried away
NewsPlayer of the Match: Who was Liverpool's star man against Southampton?
ReactionDominik Szoboszlai: We answered another question - we just have to keep going
NewsMohamed Salah becomes third Liverpool player to score 100 away goals
StreamWatch in full: Women's League Cup - Newcastle 1-6 Liverpool