Half-time substitute Steven Gerrard was sent off 38 seconds into the second half for a stamp on Ander Herrera as Liverpool suffered a third home league defeat of the season.
Daniel Sturridge replied after Juan Mata’s double – Wayne Rooney also had a penalty saved by Liverpool ‘keeper Simon Mignolet in the fourth minute of second-half stoppage time -??but Liverpool missed the chance to go above United into fourth place.
Instead, Rodgers’ fifth-placed side are now five points adrift, but the Northern Irishman insists there is plenty of time left to gatecrash the current top four with eight matches left to play.
“We had a 10-game objective that we set,” said Rodgers. “Built into that was that we were not going to win every single game.
“It’s still very much possible for us to go where we want to go, which is the top four. We just need to fight that bit harder and make up a five-point difference.”
The defeat was Liverpool’s first in the league since the 3-0 loss against United at Old Trafford on December 14 – ending a 13-game unbeaten league run for Rodgers’ side.
“That last performance at Old Trafford was a great springboard for us,” he said. “So now we must use this similarly – refocus, get over the disappointment and then come back into a tough game next against Arsenal and really look to get the points there.”
Liverpool next face Arsenal at the Emirates Stadium on April 4.
Rodgers was happy with his players’ efforts, if not the overall display or outcome, against United.
“I think it was clear that in the first half we gave them too much room,” said Rodgers. “They were able to control the game much better than us and they deserved the lead at half-time.
“Second half, we looked to change it. Obviously, we went down to 10 men early. But then I thought the players really demonstrated their quality, fight and spirit to keep going right to the very end.
“We went 2-0 behind against a good side. We got the goal back to 2-1 and were in the game right until the very end. I’ve got great pride in the players. I’m disappointed with the result and performance, but they’ve kept going.”