Liverpool have found the net just three times in their opening five Premier League games and were largely toothless in the defeat at Old Trafford.
Rodgers' side struggled to create chances against a resolute United defence and seemed to lack midfield creativity or forward movement.
A stunning late overhead kick from Christian Benteke, which ensured Liverpool did not fail to score for a third straight game, was the only bright spot for the visitors from an attacking perspective.
The Liverpool manager felt his side were overly keen to get the ball forward to the Belgian target man and were guilty of being too direct.
"Over the first five games creating goals is something we need to look at," Rodgers told Sky Sports. "It is too easy sometimes for us to go direct to Christian Benteke who was excellent today.
"We need to be a lot technically better than we showed today."
Liverpool have now lost back to back games, after a 3-0 home defeat by West Ham United before the international break, and have won only one of their last eight away games in the league.
It is a run that will concern Rodgers who came in for heavy criticism from sections of the fanbase after a woeful finish to last season.
"You are never happy when you lose a game especially to your rival," he added. "The only positive for me is that we had a defeat here last year and we got better.
"The key for us is to initiate a game and create chances, that is something we need to be better at."
It was always going to be a tough start to the campaign for Liverpool who must face all of last season's top five away from home before the end of November.
With seven points from their first five games, they are already eight adrift of leaders Manchester City.
(Reporting by Toby Davis,; editing by Tony Jimenez)
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