A Michael Dawson goal put the hosts ahead in the first half, as the central defender made the most of a terrible offside trap to head home a cross from the right.
Although Liverpool pushed forward in numbers as the match wore on they never looked like breaking down Hull's massed defensive ranks.
“We just lacked that killer instinct in the final third. We are disappointed with the goal,” Rodgers told the BBC.
“Apart from that we didn't have too many chances against us. It was poor defending from us. We didn't come out together and Dawson is onside.
“We were never enough of a threat. It's been a mark of the season really, in that final third we have struggled.”
Liverpool's troubles in front of goal have been endemic throughout the campaign following the departure of Luis Suarez to Barcelona and Daniel Sturridge's continuing injury woes that have kept him out for most of the season.
The club's inability to adequately replace Suarez in the close season and a recruitment policy that brought in a number of players who have failed to shine in their debut campaigns has been a recurring theme.
Mario Balotelli, who has come to represent the failings of Liverpool's close season transfer policy, was deployed as a lone striker at Hull before being replaced in the second half.
It was another ineffective game from the Italy forward, who never looked like adding to his solitary league goal this term.
The defeat left Liverpool fifth and seven points adrift of the top four and a Champions League qualification spot.
“I think that (the top four) is not the reality of it,” Rodgers added.
“Our fight is to perform better through to the end of the season. It was always going to be difficult for us. The opportunity was tough this year in terms of where we were at as a team.”
Rodgers is under pressure to prove in Liverpool's remaining four games that he can continue to take the club forward as he could find his role under scrutiny at the end of the campaign.
Liverpool host struggling Queens Park Rangers on Saturday. – Reuters
Original source: Liverpool struggling to score