Liverpool made the short trip to their bitter rivals seeking a swift response to their UEFA Champions League exit courtesy of a 1-1 draw with Basel on Tuesday.
However, goals from Wayne Rooney and Juan Mata put the hosts into a 2-0 half-time lead before Robin van Persie added a third in the second half to help United to a sixth consecutive Premier League victory.
The visitors were left to rue a series of missed opportunities, though, with United goalkeeper De Gea winning the man-of-the-match award for a string of impressive saves - Raheem Sterling and Mario Balotelli both finding the Spain international in top form.
Liverpool manager Rodgers was happy with the attacking intent his side showed, but conceded a combination of De Gea's excellent form and poor defending contributed to their seventh top-flight defeat of the campaign.
"I thought we did enough to win the game," he told Sky Sports. "It epitomised our season really, we're not prolific enough in goalscoring.
"Credit to the players we created enough chances, I thought De Gea was man of the match, I've seen him have four or five games like that.
"We created enough chances to win the game, that was pleasing, but we made defensive mistakes and that cost us.
"The players tried to fight, continued to press but we couldn't take our chances."
The result was a reverse of Liverpool's 3-0 victory in the corresponding fixture last season and Rodgers bemoaned the sloppy errors that saw his players on the losing side this time around.
"It's always frustrating especially when you come here," he added.
"In the first half we were down and I thought we were the better side. But you can't concede goals like we did.
"You can't lose your runner for the first like we did and the others were poor as well. We wanted to come here and create because we haven't done that this season."
