The Foxes are fifth in the Premier League and welcome third-placed United in the final game on Sunday.
Victory would return Leicester to the Champions League next season but Rodgers feels the heat is on United.
Rodgers said: “I think there is a difference where we want to be in the Champions League. We would love to be able to do that but when you are a club like Manchester United, or one of those super clubs, there is a need to be in the Champions League for many reasons.
“That is pretty clear. For us we would want to be in it. We will give everything we can. If we fall short then we have still had a really good season in the first season we have been together.
“When you are at that level of spend and everything else there is a need to be in there and that brings a different level of expectation.”