The 40-year-old, who guided the Reds to seventh last term, feels his side now needs no more than a couple of additions to reach their target.
He told The Daily Mirror: "I'm not here to be comfortable, to sit and earn the money and just enjoy being Liverpool manager.
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"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.
"What we showed last season was promise. There were moments of disappointment and moments of delight, but when I look at the reality of it we scored 47 goals the year before and this time got 71 - and we hope to add to that amount."
Spanish forward Iago Aspas is set to complete a move to Anfield from Celta Vigo at some point this week, but Rodgers does not intend to stop his summer spending there.
"Defensively, for a team that was supposed to be very strong a year earlier, we only conceded three more goals," he added.
"So in terms of numbers and performance wise we improved. Now I believe we will improve again - and we have to because we want to sustain a challenge and aim higher every season.
"We need one/two centre-halves, and I'm looking to bring 20 more goals into the team - so I'm also looking at an offensive player to give us a real threat on goal and another attacking midfield player.
"We definitely need to do that, especially if we're going to put some young ones out on loan to gain experience."