The 22-year-old, who competed for Team GB at the London Olympic Games this summer, was praised for his performance during Liverpool's 2-2 draw with Manchester City on Sunday.
"When you make big-money signings people expect it to take time to settle in," Gerrard told the club's official website. "You naturally give them that bit of time but it seems like Joe has cruised in and settled in really, really well.
"He is only small but he passes the ball well, he's safe in possession, he works really hard for the team. If he can keep performing to the level he is then I think we've found ourselves a player."
Allen moved to Anfield from Swansea City for a reported £15m earlier this month.