Alexander-Arnold this season has made 17 appearances in all competitions while scoring three goals - all at the age of just 19.
Gerrard told Liverpoolfc.com: "[I'm] very pleased but not surprised.
"I worked with Trent when he was a kid before he progressed into the first team and it's no shock or surprise to me that he's finding his consistency.
"I thought he was excellent at the weekend; for a kid so young to actually see and then to execute the passes that he's playing in the final third, that shows his confidence, it shows the confidence that the manager has got in him.
"What you've got to remember is, Trent's body is going to change. He's going to get fitter, he's going to get stronger, he's going to get more experienced.
"He's going to get better and better, which is a very exciting thought for all Liverpool fans."