The England international opted against a contract extension at his boyhood club last summer in favour of a new challenge in La Liga.
After initially negotiating a free transfer move to Madrid, Los Blancos eventually paid around £10 million to remove Alexander-Arnold from the final weeks of his contract, to be registered in time for the FIFA Club World Cup.
His decision to move on and plenty of supporter frustration over how he handled his departure created a rift and the 27-year-old admitted it's impacted his mixed form in Spain.
"The booing and disappointment from Liverpool supporters is something I'm absolutely able to shoulder. I can understand it, in my own way," he told an interview with the Mirror.
"But I hope one day there'll be a degree of understanding about the decisions I wanted to make around my own life.
"It hurts because of how much I've put into the club over the course of 20 years and the sacrifices I made during that period. It hurts."
Alexander-Arnold started on the bench in Real Madrid's 2026/27 season opener as Jose Mourinho opted for Denzel Dumfries at right-back in a 2-1 win at Espanyol.