Alexander-Arnold has come under heavy criticism for his recent performances, appearing more vulnerable in defence, losing the ball more often and not providing the assists that almost became his trademark in the final third.
"We too easily forget that Trent Alexander-Arnold is only 22," Carragher wrote in The Telegraph.
"Trent could do worse than share a private call with Steven Gerrard.
"I remember well how Stevie overcame a slight dip after his first initial breakthrough into the first team, guided back to his best. It happens."
Gerrard made his debut for Liverpool in 1998 with similar hype around his career, and after having a dip in form became a key cog in the side that won the League Cup, FA Cup and UEFA Cup just three years later.