Long-serving defender Carragher admits it is time for the Reds to prove their title credentials by taking three points off the current champions.
"We haven't beaten either of our rivals this season and we need to change that," said Carragher in an interview with Zoo magazine.
"The draws against Arsenal and Chelsea felt like defeats because in both games we took the lead.
Carragher also wants Liverpool to repeat last season's home performance against United, despite John O'Shea scoring an injury-time winner for the Red Devils.
He added, in reference to United's players celebrating on the Anfield pitch: "I was so angry after the game, I went straight off the pitch. I didn't see any of that until I watched it later.
"You can't blame them. If we won such an important game at Old Trafford, we'd be going nuts.
"We played really well that day, made plenty of chances and United had Paul Scholes sent off, so it was a bitter blow.
"Having said that, if you were to say to me now that we'll perform the same on Sunday as we did that day, I'd take it.
"If we create the same amount of chances, I'd fancy us to take them."
