The experienced Denmark international has found it difficult to adapt to the demands of the Premier League following his move from Juventus in the summer.
He admits the first few months of his Reds career have not gone to plan but is working hard to get up to speed.
"I'm still trying to settle in. I have only been here for three months and it has been a very hard start, not just for me but also for the club," he said.
"We are struggling to get back up the league and I haven't done as well as I would have liked.
"There have been many changes here. The coach is new, the owners are new and it is up to me to keep learning about how to play in the Premier League.
"I'm trying to work hard at Melwood and I hope that I can help the team in the future.
"I'm trying to do my best every single day. I know Liverpool are a great club and I hope that, after some time, I can improve and I can be help for the team.
"Do I feel I have to prove myself? Yes, for sure. I have got to work harder because I have been brought in.
"People knew that I played for Juventus but that still means I have got to earn my stripes here.
"I want to show the fans that I can help the team and I am a good player."
Poulsen is conscious, however, his form is secondary to that of the team and although the draw at Wigan on Wednesday - when the Dane came on for the last 20 minutes - was disappointing it extended their unbeaten run to six matches in all competition.
Another tough test awaits against Stoke at the Britannia Stadium and the midfielder knows how important it is to lift the performance and energy levels.
"It is not about me. The team is always the most important thing," he added.
"We have had four victories in a row before Wigan and though we stepped down there, we are looking to change that back when we play Stoke.
"We want to get back to the levels we showed against Chelsea.
"You can't really afford to let your level dip. The Premier League is very tough and this year you are seeing that every team can beat each other.
"I know people say it all the time but there are no easy games.
"I know it will be difficult at Stoke. They have some special qualities, from the long throws so it will be a tough test.
"But when we play our best football we keep it on the ground and I hope we can manage to press our style on them."