The Reds were without injured Daniel Sturridge and fielded six summer signings, with four players making their home debuts.
Rodgers said: “We started slowly and gave away a poor goal.
“We picked up the tempo but we failed to open them up, and never created the chances we would normally do.”
Gabriel Agbonlahor put Villa ahead from a corner in the ninth minute and the visitors worked hard to defend their lead, limiting Liverpool’s chances.
“You have to give Villa credit,” added Rodgers. “They defended really well once we got the ball and we could not find the final pass. It was really frustrating for us.
“We started the game really slowly, which is unlike us, but it was our lack of quality with our final ball and in the final third that let us down.
“Games like this can happen when players are getting to know each other but we had new players when we played against Tottenham two weeks ago, when we were outstanding.”
Rodgers surprisingly rested Raheem Sterling, who came on as a substitute in the second half and claimed his team’s schedule of seven games in 21 days required him to rotate his squad.
“We have got a big couple of months coming up and, looking at that, I thought this game was one where I could rest him,” Rodgers explained.
“If he had not played international football for England last week that would not have been the case – he came on and he was bright, and he will certainly play on Tuesday night [in the Champions League].”
He also added that his team wasn’t distracted by Tuesday’s return to the Champion’s League Football, as Bulgarian side Ludogorets visit Anfield.
“There has been no thought of that game at all,” Rodgers added. “We are very much about taking one game at a time. This is a very honest group of players and they gave everything against Villa.
“There is nothing better after a disappointing performance and result to get going again on Tuesday in a competition we love and hopefully we can start that competition with three points.”
