Brendan Rodgers conceded the defensive brittleness that undermined Liverpool’s title challenge last season “is still a problem” following Aston Villa’s merited 1-0 victory at Anfield.

The Liverpool manager cited a lack of quality up front for his side’s second defeat of the Premier League season but was also highly critical of the defending that enabled Gabriel Agbonlahor to score the ninth-minute winner. Liverpool have kept only one clean sheet in their last 10 matches, last season included, and Rodgers was unhappy at the roles of Mamadou Sakho and Dejan Lovren in the Villa goal. As well as the two centre-halves, Rodgers admitted the goalkeeper Simon Mignolet needs to take greater responsibility.

“It is still a problem,” said a despairing Rodgers. “We have to do better down the side of the pitch. We have to defend better, that’s where it starts. Just defend, don’t try and be clever, don’t try to play, just defend and don’t let them have the set-piece. Then, when the ball comes in the box, we lose the first duel. We were a bit unlucky with the ball bouncing off [Javier] Manquillo but we didn’t start well. They could have scored more from set-pieces. [Philippe] Senderos had a free header.”

Rodgers wants Mignolet to show more authority behind his central defenders but described Saturday’s display as a collective fault. The manager, who has been linked with a move for the former Barcelona goalkeeper Víctor Valdés, said: “We do expect the keeper to take more responsibility, but look at the last game against Spurs. We defended really well in that game and they are a much bigger side. We need to be on the front foot more. We need everyone to defend in the box and that’s something we have to be comfortable with.

“I think you can see from the goal that we need that consistency. They lost their marker too easily in the box. When you let the opponent get the first contact that’s what can happen. It was unfortunate, and Lovren is a wonderful defender, strong and aggressive, but we have to do better in that situation. The worst-case scenario should be that when we have days when we’re not creative with the ball, then we get a point and move on. That’s the disappointing thing because we didn’t and it is important for us.”

Raheem Sterling was kept on the bench for 61 minutes against Villa as Rodgers sought to protect the 19-year-old for Tuesday’s Champions League return against Ludogorets Razgrad. Rodgers handed Adam Lallana and Lazar Markovic their first starts, with Mario Balotelli making his Anfield debut, and there was a lack of fluency to their attacking play until Sterling’s introduction.

Rodgers said: “In attacking positions we have the quality but just couldn’t find anything against Villa. It’s something that has got to happen. I trust the players implicitly to do that. These players have a very strong mentality and are bitterly disappointed because they gave everything but when you start slowly like we did, and give away a poor goal, then you’re up against it.”