Crooks named Alexander-Arnold in his team of the week on the BBC Sport website, explaining: "This lad gets better every time I see him. Against a dogged Brighton, the Liverpool and England full-back showed a maturity well beyond his years.
"I was surprised to see Arnold standing on his own ready to take the free-kick that hit the bar while Mohamed Salah and James Milner stood and watched."
Alexander-Arnold has helped Liverpool to three clean sheets in their first three games of the season, but Crooks explained that it has been Alexander-Arnold's ability on the ball - rather than his defensive displays - that have been the most exciting to see, saying: "Alexander-Arnold is a defender who loves to play [the ball] forward, not square or back, because he's not afraid and has the talent to do it.
"But the moment of the match for me was the 40-yard pass to the feet of Salah on the other side of the pitch. I thought I'd died and gone to heaven. What a ball."
Crooks also included Alexander-Arnold's Liverpool teammate James Milner in his team of the week, saying: "The way the Liverpool captain pounced on Brighton's Yves Bissouma was reminiscent of a cobra and with a bite to match.
Brighton's error cost them the fixture. The way Leon Balogun gave Bissouma the ball in such a difficult position with his back to the play lacked any thought or consideration for his team-mate."