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The right-back came on as a substitute during the 1-1 Premier League draw with Crystal Palace on Sunday afternoon.
Alexander-Arnold was warmly applauded both during the match and before their trophy presentation when his name was announced.
During the celebrations, he was visibly emotional when joined by his friends and family on the pitch at Anfield.
"I didn't know what to expect stepping out at Anfield after what had happened a few weeks ago, but I wanted to play for the club one more time," he told Sky Sports.
"And I said that to the manager, and he trusted me to go in at half-time.
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"To get the reception I got means more than anything to me.
I've played hundreds of games for the club, but I've never felt so loved and so cared for than now.
"From the bottom of my heart, I hope that one day, the fans and supporters of this club will be able to recognise the hard work and everything that I've done for the team.
"Because there wasn't a day, a minute or a second that I didn't think about the team, from six years old to 26 now.
Twenty years is a very, very long time, but I've loved every single minute of it.
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"The ups and the downs, coming through the academy, making it to the first team, and then being part of the first team properly.
It's been an honour and a privilege for me to be part of this club."
Taking to Instagram on Monday, he shared a heartfelt message with fans.
"Fairytale ending," he wrote, followed by a love heart.
The likes of Cody Gakpo and Kostas Tsimikas were among those to comment, while several Reds' stars including Diogo Jota, Ibrahima Konate, Andy Robertson, Alexis Mac Allister, Federico Chiesa and Dominik Szoboszlai all 'liked' the post.
They weren't the only ones, either, with Bellingham also leaving a 'like' ahead of their likely reunion at the Santiago Bernabeu this summer.
Following confirmation from Alexander-Arnold that he will leave Anfield last month, Real made an initial approach to Liverpool over signing him in time for the Club World Cup.
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The 26-year-old's Anfield deal expires officially on June 30, but the Spanish club would like to have him in the squad for the summer tournament in the United States.