David Moyes' men are nine points behind fourth-placed Manchester City going into Sunday's match against the Reds but their city rivals have two games in hand and the champions are 11 points behind Arsenal and Liverpool, who have played the same number of games.
That means United will need a remarkable sequence of results in the closing stages of the season if they are to make Europe's elite competition, while Liverpool are currently on course to return to the top table for the first time in four years.
And Rodgers believes a lack of Champions League football means United, who made the final three times in four years between 2008 and 2011, will struggle to attract the calibre of players required to get them back to the top.
"We still have a lot of work to get in to the Champions League," he told various national newspapers. "But when you're not in it, even though this club is a worldwide, monumental club, we found it difficult because the best players want to play in the best competitions.
"This was Liverpool and we weren't in the Champions League. In order to get in some of the type of players we want, that's where we need to be and we're trying to be.
"Any club will suffer the same when they're not in there. There is no doubt it will hurt you, but they (United) will know that."
Liverpool won the Champions League title in 2005 but have not won the English top flight since 1990 and Rodgers has warned that United could face a similar drought after dominating English football for two decades.
"We were talking about the great Liverpool teams - one year becomes two and then all of a sudden it was 20 years since they won the title," he added. "It can get away from you very quickly.
"It's our focus and drive to arrive back (in the Champions League). We have a long way to go but have shown great potential to be in there. I believe if we can get to that level then it gives us a massive advantage as a club."
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