The striker has conceded that it will take time to get used to the new manager's game plan, but is determined to become one of the leading goalscorers in the Premier League
The Uruguayan told reporters: "We certainly need to win this one.
"I have only one league goal so far and it will be difficult if I do not improve.
"Nobody is content with our Premier League results so far. Things have not gone as the coach wanted and we are obliged to react accordingly.
“We didn’t want this situation in the first few weeks but we must win to reduce the gap to our rivals and dedicate a good triumph to our fans.
“There are no nerves in the dressing room. Only frustration."
Suarez, 25, is effectively the club's lone striker after the club allowed Andy Carroll to join West Ham on a season-long loan without buying a replacement.
Commenting on Carroll's departure, Suarez admitted: “I was happy playing with Andy but he has gone.
“I think only of playing well, of victories and of winning trophies. My challenge is to keep improving."
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He also confirmed that despite speculation about his own future while the transfer window was open, he is fully committed to the Anfield cause.
“During this summer there were many rumours about my future.
“But I never doubted my continuing with Liverpool. Clubs asked about me but my objective is to try for more success here. We want to make the Champions League and to fight for other honours. I am convinced that if we can win two consecutive matches, everything will change.”
So far Liverpool have only managed to secure one point from three games, having suffered defeats against West Brom and Arsenal. Although the side secured a home draw against Premier League champions Manchester City, they had led on two occasions, before a misplaced pass by Martin Skrtel gifted Carlos Tevez an equaliser.
But despite the Reds' League from, Suarez stresses that he is happy with new boss Rodgers. He said: "He has confidence in me and I want to reward that with goals. He wants us to play a passing game and I'm optimistic it will work.
"Training is not so different from under Kenny Dalglish but Rodgers insists on more touches on the ball whereas Dalglish wanted a more direct game.
"Under a new coach, we must adapt to his style and carry out his orders. I'm going to do that."
As well as targeting Champions League qualification with Liverpool, Suarez has revealed he is aiming to meet a personal challenge, too.
"My aim is to be one of the best goalscorers in the Premier League but, at the moment, I have one goal.
"I've scored three times against Sunderland and want another goal against them. Liverpool need the win."