Gudjohnsen said that everyone feels the pressure, since the take over.
He said: "We are Chelsea Football Club. Everyone is under pressure. Especially the way we are heading, there will always be pressure to win things.
"That is not only on the manager but on the squad. We are all fighting, all wanting to show that we want to be part of this changes and that we want to be part of the team.
"If Chelsea are heading this way, personally I would love to be part of it. But I do know that I am under pressure to show it every week.
"The new era started at the beginning of the season. Mr Kenyon coming in is part of that. You can see it in everything that is happening around the club. Things are there to help us become a big club.''
Jimmy's penalty at the weekend kept us close to Arsenal and Man United, and we still have to face Stuttgart in the Champions League and Arsenal in the FA Cup.
"We are still in three competitions. In the Premier League, there is everything to play for as we still have to play the top two,'' added Gudjohnsen.
"At the moment, we are always hoping they will drop points. But if we do our jobs, we will put pressure on them towards the end of the season, I am sure of that.
"I just want to be part of a team that wins something. We are in three competitions. We are not there to take part. We want to win.