The 26-year-old caused a stir among Liverpool fans with his decision move to their European rivals last month with Real Madrid agreeing to pay £8m to sign the player in time to compete in the tournament.
He then raised eyebrows at his official unveiling when he appeared to respond to questions in fluent Spanish, a language he admitted took “a few months” learning.
The England international started Real Madrid’s Group H opener at Hard Rock Stadium in Miami and told Flashscore: “In my mind and my heart I know I made the right decisions for me.
“Obviously it was a very proud moment for me. (I’m) very happy to have made my debut.
“(Joining Real Madrid is) something that I think most, if not all players, dream of at some point in their life.
“It’s the first time I’ve moved clubs so I didn’t know what to expect. I had no expectations coming in to this,” he said.
Federico Valverde missed a stoppage time penalty for Real Madrid, who had to settle for a 1-1 draw against their Saudi opponents in manager Xabi Alonso’s first game in charge.
It was a result that frustrated Alexander-Arnold.
“Of course there’s some disappointment,” he said. “The mentality that comes with being a Real Madrid player is wanting and expecting to win every single game.
“But, you know, new coach, some new players, new ideas, some positives to take with it especially in the second half and the foundations been built to go and win the next game.
“Course it will take a little bit of time to get used to the players and the team. It’s new to me, so it’ll take a bit of time, but I’m very happy to have played today.
“But yeah it’s a big change, a bit different, but I’m loving every single minute of it.”
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