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Liverpool travelled to Selhurst Park in the midst of a three-match losing streak in all competitions. Rodgers' side last won in the league with a 3-2 triumph at QPR on October 19 and have collected just one point since.
Goals have been in short supply this season for the Merseysiders since the departure of striker Luis Suarez to Barcelona.
Rodgers said: "We're low on confidence at the moment in terms of the results and I think that sort of tempo and intensity of our game has just dropped right off and obviously we concede pure goals but we have no one to blame but ourselves.
"As the manager I take full responsibility for that.
"We aim to be tighter and more resolute defensively. Obviously we get the goal – and a number of the games this season – we've led a goal in front, and that should be enough.
"We work on defending, we work very hard on being compact, but we never managed the game.
"We've got a lot of young players and players who are new to the club but we have to be better than that."
What should Rodgers have done differently at Selhurst Park on Sunday? Let us know your post-match thoughts in the comments section below.