But Reds boss still believes the midfielder is a quality player
The 30-year-old midfielder arrived on Merseyside after making a £4.5 million switch from Juventus, and has since turned in a few under-par performances at Anfield.
His recent introduction into the game against Wigan Athletic was not welcomed by a section of the travelling fans, but manager Roy Hodgson believes that the Dane was pivotal in securing a draw for his side.
"He was good against Wigan, his introduction secured the point at least because he was very good when he came on," Hodgson said, according to The Guardian.
"Unfortunately I can't do anything about the fans, but he's had one or two games in front of our crowd where he's not played well and he knows he hasn't. He is devastated by that and the crowd, who aren't stupid, know he's not played well. It's a fact of life.
"He can only keep working hard and when he gets his chance he has to get on with his job. He had a job to do against Wigan and without his introduction, with a very tired Maxi Rodriguez and Dirk Kuyt, who knows we could even have lost the game.
"But he's got quality, he's a good defensive midfield player. He's not that bad on the ball, but let's not beat about the bush and try to disguise the fact – he's had a bad start."
Goal.com recently revealed exclusively that the club could sell Poulsen in January.