The Reds boss felt poor decision making was to blame for the defeat, inflicted by goalscorers Lukas Podolski and Santi Cazorla.
"It's about decision making," said Rodgers. "The goals we conceded, it's got nothing to do with style, nothing to do with systems, nothing to do with the tactical element of the game. We gave the ball away and then we didn't recover well enough to stop the shot.
"For the second goal, we had enough bodies behind the ball to defend the goal.
"And we created enough chances but were not clinical enough. There is a lot of good to come from the game but we lost and we need to improve.
"We'll get better as our season progresses. It was always going to be a difficult start.
"I have an inherent belief in this way of working, and I've had success with it. Over time here, that will be the same. These are the hard yards that you've got to put in early on and take the flak for."