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The Reds were left 24 points behind their rivals in the Premier League after a 2-1 defeat at Old Trafford.
But Rodgers insisted: "We are 24 points behind Manchester United but we are not 24 points behind in quality. The difference is down to the squad.
"Once we close the gap in the squad I have great hope we will be able to challenge. Today's an example of that."
Robin van Persie and Nemanja Vidic scored in United's 2-1 win victory that opened up a 10-point lead at the top of Premier League ahead of Manchester City's visit to Arsenal.
Liverpool's £12m signing Daniel Sturridge pulled a goal back and looked lively as a second half substitute.
And Rodgers said: "I thought by the end we deserved something. I was proud of the fight in the team once we went 2-0 down. We were disappointing in the first half, too tentative.
"When you come to a place like this you have to have courage and belief and we were too tentative."
Rodgers, however, was impressed with Sturridge, saying: "This boy is going to be a real top striker in this country and he is going to score many goals for Liverpool.
"The boy is a goalscorer. I have been assessing him in training and sometimes you can rush players back and break them.
"I didn't want to do that, but he is certainly getting there."
Rodgers added: "In the second half, after we conceded the goal, we could have given up the fight but that is nature of the group.
"In the end, I thought we maybe deserved something from the game.
"The goals we conceded were disappointing. We will learn from days like today, even though we didn't get the result.
"In the first half we never threatened enough. There weren't too many chances either way and the ones they had we presented to them."
Liverpool manager Brendan Rodgers is confident they can close the gap on Manchester United over the long-term.