Andy Reid created the winner with a precise through-ball which put Ched Evans clean through on goal and the former Manchester City man clipped an early shot wide of Dorus De Vries and into the corner.
"I thought we deserved something from the game," said Rodgers.
"We controlled the first half and then a lapse of concentration gave them something to hang onto.
"To be fair, though, we did lack our usual intensity. That was something I emphasised at half-time. We are going to lose some games though.
"From our point of view it was a bad goal to give away, from United's it will have been excellent. It was superb pass from Andy Reid. Few players could do that in this division. And then it was an excellent touch and finish from Ched Evans."
Source: PA
Source: PA