Gerrard made his 600th appearance for the Reds on Sunday against Newcastle United.
McAllister told Liverpoolfc.com: "It was very clear to me, even in the first couple of weeks of arriving here, you could see he was a very special young player. Somebody that was growing into the position.
"He's not let anybody down and proved to be very influential for both club and country. He's had some very special moments for his beloved Liverpool.
"It really is a fantastic achievement [to reach 600 games]. Over the last 10/12 years he's proved to be such a wonderful servant and a great player as well.
"He's a proud captain and a very proud Liverpool player.
"It's very nice to be asked by the club to come up and present this.
"He's a good friend and I think he thoroughly deserves it. Let's hope he can go and get another couple of hundred of games!"