United are currently nine points off the top four and have struggled for consistency in David Moyes' first season at the helm, with a spot in the UEFA Champions League in doubt.
Their best chance of reaching next season's Champions League may be to win this year's edition, though they are facing elimination at the first knockout stage after a 2-0 first leg defeat at Olympiacos last week.
And Rodgers, who has led Liverpool to a challenge at the top of the table this season, believes the Anfield club's recent struggles to mount a serious challenge could prove to be a precursor for United ahead of the sides' meeting at Old Trafford on Sunday.
Liverpool have not finished in the top four since 2009, and Rodgers believes a lack of Champions League football has hampered them in their efforts to regain a place at Europe's top table.
He said: "We still have a lot of work to get in to the Champions League. 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 will know that.
"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. 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."
