The Reds' victory at Old Trafford was their fifth in a row in the league, a run which has taken them firmly into title contention.
And the Reds boss admits that their win over the reigning champions was so dominant that they will have sent out a message to everyone.
"It was a big statement. Old Trafford has been a notoriously difficult place over many years but we played with such dominance," he told the Liverpool Echo.
"It was United's ground, mostly their supporters but it was our ball. We controlled the game.
"We had a beautiful arrogance in our game. The intensity at which we pressed and some of the imagination in our football was great. Defensively, we were very strong.
"We showed the level we're at in terms of work-rate both with and without the ball. We came off Old Trafford thinking we won 3-0 but could have had five or six. When we played at home against Arsenal we scored five but could have had seven or eight.
"We got five away to Tottenham when it could have been six or seven, and four at home to Everton when it could have been six or seven. It's remarkable when you put it into context.
"As manager, it's great to lead these players into these arenas and see them perform like that. The neutrals are looking at us and enjoying what they're seeing."
Despite their United success, Rodgers insists that will mean nothing if they slip up at Cardiff City this weekend - a game they are now 100 per cent focused on.
"Last weekend was a brilliant day for the supporters but after a couple of days to enjoy it, it's been back to work this week," he said.
"All our focus is purely on Cardiff City. That has been our world this week. There have been no thoughts of anything else.
"We haven't talked about the title, we're just enjoying how we are playing and working.
"For me it's always been about the next game. There is no point worrying about Sunderland next Wednesday when we've got a massive game on Saturday.
"The pressure and expectation doesn't change when you play for Liverpool - it's there both home and away every game.
"It's great for the supporters to be dreaming and they take great pride in what they're seeing. The level of our game is improving all the time but we haven't achieved anything yet.
"It's been a difficult season for Cardiff but they have some excellent players and I know it will be a tough game. If we keep the intensity, the foundation of our work and play with the control we have done then it gives us the opportunity to get another three points."
Rodgers insists that his players need the credit for their success this season, with the work they are putting in.
"We have a plan for each player and we're committed to helping them become the best they can be, but it's the players' responsibility. The crown is on their head - they are the kings of their own destiny," he said.
"If they listen and learn like they have been doing then in this environment they can only improve."