The Brazilian curled in a stunning effort from outside the area at Anfield on Sunday to seal a 2-1 victory for Brendan Rodgers' side.
Coutinho also netted the winner in the corresponding fixture last season, and his latest strike added to further recent wonder-goals against Bolton Wanderers and Southampton.
"He's so good," Allen told the Liverpool Echo.
"With his performances recently, Philippe has taken things to the next level. The Brazilian team is obviously full of talent but he has to be really pushing for that.
"Working with him day in, day out, he shows his quality every time he trains and plays and he scored a superb winner to get us the three points.
"He's skilful and very versatile. He can play in different positions and teams are struggling to deal with him.
"Why has he started scoring? I think it's confidence. That's a huge thing in football.
"The ability has always been there. Technically, he's right up there.
"I think some people forget how young he is at times. He's a young player getting better all the time.
"He's showing that goals are part of his game. He was always on this path.
"Those of us who work with him on a daily basis, we always knew he was going to kick on and reach this kind of level."
