Allen arrived from Swansea City this summer in a £15 million deal.
Gerrard told liverpoolfc.com: "When you make big-money signings people expect it to take time to settle in. 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."