Rodgers' comments come during the ongoing contract saga involving striker Raheem Sterling, who has decided against signing a new 100,000-pound-per-week contract.
Rodgers also conceded that high-profile players are more likely to sign with clubs that will finish in the top four and qualify for the Champions League.
"Most players want to be in the Champions League, but I think also that Liverpool is a great club," he told PA Sport. "I said that before I came into the job, and it is been even more rubber-stamped now that I have been here for two-and-a-half-years.
"Liverpool is a phenomenal club that players want to play for, but, of course, players want to play at the top level of the game and if you are not in the Champions League it makes it difficult for you.
"We know that, but we just have to continue to fight in order to be a stable club in there — and we will continue to do that."
Rodgers is also wary of the fact that Liverpool will have to set their sights on qualifying for the Europa League unless Arsenal, Manchester United or Manchester City falter in their run to finish in the top four.
The 42-year-old has also urged his side to avenge their 4-1 loss to Arsenal on Saturday by beating Blackburn Rovers in a FA Cup quarter-finals replay at Ewood Park on Wednesday.
"We want to be in the Champions League, that is important and it is key for us, but it is highly unlikely this year," he said. "I wouldn't expect the others to slip up, then add to that the growing number [of players] we have got unavailable and I think it will make it very, very difficult.
"We always felt this year was going to be difficult, that was the reality of it.
"Our run last year nearly brought us the title. We lost a world-class player [Luis Suarez] and lots of other developments that happened within the club.
"But it is frustrating that we got ourselves in a position over the last three months, very close, to then come up short in the past two games.
"However, I look at Arsenal and their bench, the players, the world-class players on the field with big talent and it shows the continual work we have to do.
"It is going to be a little like this, until we become more stable, we have got young players who are growing, getting more experience and then hopefully there will be a period where we qualify again."