The 21-year-old made his Anfield debut against the defending Premier League champions after completing a £15m move from Swansea City to the Merseyside outfit earlier this month.
And Liverpool captain Gerrard has been impressed by how fast Allen has settled at the Reds.
“When you make big-money signings people expect it to take time to settle in,” Gerrard told Liverpool’s 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.”
The 32-year-old was also pleased by Liverpool’s reaction against Roberto Mancini’s side after the Reds were beaten 3-0 by West Bromwich Albion in their opening Premier League game.
“There are plenty of positives to take from that game,” he added.
“When you play so well and you only get a draw, it does feel like a defeat, but no one is down after that – it was a great reaction after the West Brom result.
“From Pepe up to Luis, everyone performed well. We’re really pleased.
“If we can use that as a benchmark for our performances moving forward I think we can do really well.”
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