Liverpool produced a dominant first-half display but the home side failed to make their possession count, with Christian Benteke putting Villa ahead in 29th minute.
Andreas Weimann extended the visitors’ lead when the midfielder combined with Benteke to unlock Liverpool’s creaking defence and fire past Pepe Reina just before half-time.
Matters then worsened for Rodgers’ side after Benteke netted his second of the game to seal three points, with Steven Gerrard scoring a late consolation.
“It’s a disappointing result and performance from us,” Rodgers told BBC Sport.
“I don’t know where that came from as it’s not been like us. We were careless with our final ball and didn’t end up taking our chances.
“We will have to take that as a bad day at the office and move on. I felt today we probably weren’t quite sharp enough.
“It was a clear penalty [when Ciaran Clark pulled Daniel Agger’s shirt] and if you get that it is 2-1 and the pressure can start to build.
“But they got their third and we went a bit flat. Overall, we didn’t do enough and we must learn from it and move on.”
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