The Liverpool manager has lost both clashes with the Premier League champions since taking over at Anfield last summer.
Rodgers told the club's website: "Liverpool [versus] Manchester United is a massive game. It's more than a football game, it's a story of two cities and you're representing the people of your city and the history of that city.
"It's more than a football match. But it's important that you retain that calmness and belief on the field, to get the result, because, ultimately, that's what it's about.
"There's an intense rivalry there. I've experienced both games now as Liverpool manager, United and the Everton game. There's something a wee bit more intense in this rivalry."
Liverpool face David Moyes's side at Old Trafford on Sunday.