For long periods at Old Trafford Liverpool dictated possession but failed to convert numerous chances against an inspired David De Gea.
United on the other hand were clinical and unerring when given the chance and ruefully exposed their wounded rivals who are languishing in mid-table.
Wayne Rooney fired home a 12th minute opener before Juan Mata doubled the lead, albeit from an offside position, with a header five minutes before halftime.
Robin van Persie capitalised on a miscued Dejan Lovren clearance to add a third in the 71st minute to seal United's sixth successive league win.
Last season's runners-up Liverpool have now lost seven Premier League games this campaign and trail leaders Chelsea by 18 points after 16 games.
Their 21 points represents their lowest return at this stage of a season since the 1964-65 campaign.
"I thought we had done enough to win the game, it epitomised our season really. I'll keep searching for the solutions," Rodgers told Sky Sports.
"It's been difficult this year but that's the way it works. It's clear we haven't scored or created enough goals."
Liverpool's regression this season has been almost as dramatic as their progression last season.
Their inadequacies are glaringly obvious.
They lack a commanding goalkeeper, a defensive leader and are bereft of a forward capable of providing the goals of the departed Luis Suarez or the injured Daniel Sturridge.
On Sunday Rodgers opted not to play a recognised striker and instead tasked 20-year-old Raheem Sterling with shouldering their attacking burden.
Sterling is undoubtedly an exciting talent but against arguably the Premier League's best goalkeeper in De Gea he was thwarted numerous times and failed to prove he is capable of filling the void.
"Today, we created opportunities which we haven't been doing," Rodgers added. "We also made defensive mistakes and that cost us today. We've just got to keep working. We came here last season and it was the reverse scoreline.
"Today we were the better side in the first half but you can't concede the goals we did."
Rodgers said he "does not feel any additional pressure" after the defeat but faces a testing League Cup tie away at Championship (second tier) leaders Bournemouth on Wednesday before the visit of Arsenal next weekend.
(Reporting By Tom Hayward; editing by Martyn Herman)
Share
