Goals from Wayne Rooney, Juan Mata and Robin van Persie secured a sixth consecutive win for United, but it was De Gea who took the plaudits at Old Trafford after a string of spectacular saves.
Defeat left Liverpool 10 points below United and seven points off the Champions League places, and Rodgers felt his team might have taken something from the game had it not been for De Gea’s razor-sharp reflexes.
“We created so many chances today and David De Gea was man of the match. He’s had four or five games like that this season,” Rodgers told Sky Sports.
“David’s a top-class goalkeeper and his ability to make saves is outstanding, but his distribution is also excellent. He knows when to go short and when to go long.”
Defeat completed a bleak week for Liverpool, who were eliminated from the Champions League after a 1-1 draw with Basel on Tuesday, but Rodgers was encouraged by the number of chances his players had created.
“Today we created opportunities, which we haven’t been doing,” added the Northern Irishman, who lost defender Glen Johnson to a groin injury mid-way through the first half.
“I’ll keep searching for the solutions. It’s been difficult this year, but that’s the way it works. It’s clear we haven’t scored or created enough goals.”
United managed Louis van Gaal, whose side closed to within eight points of leaders Chelsea, conceded that De Gea’s brilliance had helped conceal the hosts’ shortcomings.
“I’m proud we have a clean sheet, but that is also because David de Gea has superb reactions,” he told the BBC.
“We gave unnecessary balls away today. That’s not good. I will ask the players tomorrow why.
“I’m very happy, but the next match at Aston Villa is important. We have had difficulty in away matches.”
Van Gaal revealed that Marcos Rojo had sustained an injury in training, which meant that midfielder Michael Carrick was redeployed in central defence alongside Jonny Evans and the fit-again Phil Jones.
De Gea’s display also earned praise from United goal-scorer Van Persie, who said: “David was outstanding. He was brilliant — it’s not often a team wins 3-0 and the goalkeeper is man of the match.”
Mata’s 40th-minute goal left a bone of contention for Liverpool to gnaw on as he appeared to have been offside when he scored after Van Persie applied a faint touch to Ashley Young’s in-swinging cross.
Van Persie confirmed that the goal should have not have stood, saying: “I have to be honest, I had a touch on that cross. But you can put that down as an assist!”