Alexander-Arnold, who has made 231 Premier League appearances for Liverpool, had praised Slot's coaching at the weekend, saying he welcomed criticism from the Dutchman.
"I think we all remember the day that Jurgen left and what that man meant to him... so to hear him say this about his new manager is always nice," Slot told reporters on Tuesday ahead of Wednesday's League Cup third round clash with West Ham United.
"It's not always easy to come in and replace a manager like (Klopp)," he added.
Slot said he wanted to field the strongest team against West Ham as Liverpool look to defend the trophy, but will have to rotate his squad after last week's win at Milan in the Champions League and Saturday's Premier League win over Bournemouth.
Goalkeeper Alisson is out with a muscle issue, so Ireland's Caoimhin Kelleher will play instead, Slot said, adding that forward Federico Chiesa, who joined from Juventus late last month, is able to start - but not ready to play a full match.
"We would all love to win something but that's far away. We have to win this game tomorrow... it's a tough one against West Ham," the manager said.
