Gabriel Agbonlahor netted the only goal of the game after eight minutes, ensuring Rodgers remains without a home win over Villa in three attempts as Liverpool manager.
A new-look front three of recent signings Lazar Markovic, Adam Lallana and Mario Balotelli struggled to break down a stubborn Villa defence as Liverpool's attack lacked its usual fluency in the absence of Daniel Sturridge and Raheem Sterling, injured and rested respectively.
Sterling emerged from the bench with an hour played and Philippe Coutinho struck the post as Liverpool poured desperately forward in the closing stages, but Rodgers felt the damage was done at a much earlier stage.
"We started a bit slowly in the game," he told Sky Sports. "We probably only started to quicken up our tempo when we went 1-0 behind.
"I think the players gave everything today. It was probably a mixture of us not being able to find that quality in the final third of the field and Aston Villa defending well.
"Once they went 1-0 up they defended tightly with lines together; back four, goalkeeper, midfield - they all defended well together.
"We just couldn't find the final pass. We had enough of the ball but we couldn't create so much."
He added: "It's sometimes what happens in football. Normally we're a team that start very, very fast - our tempo and rhythm of the game is at a high level.
"For some reason we just didn't start like that. And, obviously, when a good team gets in front, it is difficult to break them down.
"I can't question the players in terms of their effort and commitment in the game; that was first class."
