The Northern Irishman has already added to his squad with the signing of Kolo Toure on a free transfer, with deals for Spaniards Iago Aspas and Luis Alberto reported to be close to completion.
With the additions of Philippe Coutinho and Daniel Sturridge in January, Rodgers believes that he will have a squad capable of improving markedly on last season's seventh-placed finish.
"I'm not here to be comfortable, to sit and earn the money and just enjoy being Liverpool manager," Rodgers said.
"There's a pressure that comes with it and I believe we're in a much better place to challenge [for the top four] now. I think we can do it - I believe we have built a real good base this year.
"Of course, it will be a tough ask because, as we improve, other clubs will have masses more money to do so as well. But it's not my job to look for excuses, I have to find the solutions to try to push us in there - and I believe we won't be too far away.
"I believe we will improve again - and we have to because we want to sustain a challenge and aim higher every season."
One of Rodgers' biggest issues this summer is the future of Luis Suarez, with the player again reiterating a desire to leave England.