The Merseyside club ran out 3-0 winners thanks to two penalties from Steven Gerrard - who missed a third spot-kick -and a close-range strike from Luis Suarez.
The win moves Liverpool up into second place, while Manchester United - who finished with ten men after Nemanja Vidic saw red - are languishing down in seventh.
Speaking after the victory, Rodgers admitted that his side could have easily doubled their goal tally against the Red Devils if they were more clinical in front of goal.
"Our dominance in the match was clear," he said. "We had confidence and belief coming here that we could get a result. We could arguably have scored five or six and that is testament to the quality of the players.
“We are a very aggressive team. I was very similar at Swansea with my players, we got a lot of penalties with the team there and it is the same at Liverpool.
“It is our aggression and intent to attack means we are going to be in the area and provoke more fouls.
The win over Manchester United has prompted some to suggest that Liverpool are bona fide title contenders with nine games to go.
However Rodgers is refusing to make any predictions about where his Liverpool side can end up this season.
“We won’t get carried away," he insisted. "It is a wonderful result and our confidence is high at the moment but our only focus is on the next game. If we can continue to play at the same intensity, we will continue to win games.”
While Rodgers could allow himself a smile afterwards his Manchester United counterpart could do no such thing. David Moyes was at a loss to explain the defeat - which matched the Red Devils' biggest losing margin against Liverpool at Old Trafford.
He said: "I thought there was not a great deal in it at half time. We had just started to play a bit better towards the end of the first half.
“It was important we came out in the second half and got a goal back but instead we gave one away and that made it very difficult for us. I don’t think I had even got seated in the dugout when we gave it away. We were going for it but it always left us open to a counter.”