The Foxes had won just one of their previous seven Premier League games, but remain in third and restored an eight-point advantage over fifth-placed Manchester United in the battle for a top-four finish.
"The last few games we haven't been at our level. In terms of attacking, we were much better this evening. After the first goal we went on and played very well," said Rodgers.
"Early on you could see our confidence wasn't where it has been. The only way you regain that confidence is hard work and these players have been brilliant."
Defeat leaves Villa rooted in the relegation zone and there was little from the visitors to suggest they can save themselves in the final 10 games of the season.
No side has conceded more goals in the Premier League this season than Villa.