Rodgers saw captain Steven Gerrard score twice from the penalty spot at Old Trafford before Luis Suarez added a third late on.
|10/3||Liverpool are now 10/3 with Bet365 to win the Premier League|
"It's obviously a big win over a huge rival - two of the biggest British clubs that are renowned worldwide. To dominate the game like that was very pleasing," he told reporters.
"I thought we could have had more goals, I thought we were really aggressive in our game going forward and with a better final touch or final ball we might have got in a bit better and finished them off even more so.
"We attack with great intent and we defend as well. We will just focus on our next game. I can only look at our next game. I've done that since I walked in the door."
As he approaches the end of his second season at Liverpool, Rodgers added that he expects his charges to improve as the campaign draws to a close.
This, he explained, is largely due to a change in mentality at Anfield as Liverpool eye their first league title since 1990.
"We were the same last season - we get better with the methods and that gives us confidence and belief. I try to not expect so much and let the players do the talking," he added.
"We're up there on merit so of course we have an opportunity.
"We expect to win. We have a mentality in the team that's been developing over the course of the 18 months I've been here that we expect to win, home and away.
"The belief is in the players now and you see that in their game. I haven't banned [talk of winning the title], we've just got better things to talk about.
"I don't lose sleep over it, [we] just talk about players improving their performance level and improving their life."