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The right-back was targeted by a significant section of the Anfield crowd when he came on as a substitute after confirming on Monday he will not be extending his current deal with the newly-crowned Premier League champions when it expires this summer.
Alexander-Arnold, who is expected to join Real Madrid, was subjected to loud jeers as he was introduced as a 67th-minute substitute and that continued with most of his touches.
“The thing I consider is I want to win a game of football and if we think we can win with Trent, I owe it to his team-mates and to the fans, because they (Liverpool) hired me to win as many games of football as possible,” said Slot.
“And if I think there’s a better chance of winning with Trent, then I will (pick him).
“If I think it’s a distraction or whatever can happen for us not to play a good game of football, then I might make another decision.
“But I think Trent showed today why I brought him in because he was very close with a few fantastic crosses for us to win the game.”
Alexander-Arnold looked stunned at the final whistle as team-mate Luis Diaz put a comforting arm around him.
Slot tried to put a positive spin on things by insisting the reaction was mixed but the volume of the boos suggested it was more than a minority voicing their opinions.
“It is definitely difficult for him,” the Dutchman said.
“Maybe he is positively surprised how the reactions were.
It was clear there were mixed reactions, it wasn’t all negative.
“The moment he had to take the free-kick, everybody was cheering for him to score and he was close.
“I am not sure if he has negative feelings about today…maybe, maybe, I haven’t spoken to him.”
Former Liverpool defender Jamie Carragher told Sky Sports: “Booing one of your own players while they are playing is not for me.
That was a step too far.
“That could’ve been his last performance, which might be the right thing as Liverpool don’t need a circus.”
Slot had said before the match he would not tell how fans to react and he maintained that stance afterwards.
“It a privilege to live in Europe where everyone can have his own opinion and express their own opinion and that is what we saw today,” he added.
“All of them are not happy with him leaving the club but a few of them showed it in a way that they booed him and some of them clapped.”
Alexander-Arnold’s long-time team-mate Andy Robertson told Sky Sports: “It’s not nice to see a friend get booed, it wasn’t nice.
But as I said, we can’t tell people how to act.
“I can’t tell you how I feel about it, I’m extremely proud of him.