An XI featuring six close-season signings were unable to overturn Gabriel Agbonlahor's eighth-minute opener in a frustrating outing at Anfield.
Home debutants Luzar Markovic, Adam Lallana and Mario Balotelli failed to fire as a front three and Villa were rarely troubled until Philippe Coutinho thumped a deflected shot against the post in the closing stages.
But Rodgers pointed to the 3-0 win at Tottenham on Balotelli's first appearance for the club as evidence that there will be more good days than bad.
"We played against Tottenham and we were outstanding," he said.
The players that we've brought in are very good players. We're delighted with that.
"We just failed to open them up today."
Liverpool play their first UEFA Champions League game in five years against Ludogorets on Tuesday night and it was a match that weighed on Rodgers' team selection as England forward Raheem Sterling was restricted to a substitutes' role.
Rodgers believes his playing group can cope with the extra workload they excelled without in finishing runners-up to Manchester City in the Premier League last season and he will keep faith in using all the options at his disposal.
"At the beginning of the season, I've said I've got to trust all the players that I have," he said.
"We've got a big couple of months, a really exciting couple of months coming up.
"Looking at it, this was a game where I felt we could do that.
"If [Sterling] didn't have international football then it would have been a different case.
"He came on, he was bright. He's a big player for us.
"We've built a squad here so that I trust all the players. As a team and a squad we just didn't deliver today. [Sterling]will certainly play on Tuesday night."
