Jamie Vardy scored twice to inspire the Foxes to a 4-1 victory to set a new club record of eight straight top-flight wins.
They are second, six clear of Manchester City, and Rodgers is relaxed about Leicester’s place among the leaders.
He said: “I don’t think anyone expects us to be near the top. After Manchester United won at Manchester City on Saturday, the caption came up about how far City are away from Liverpool.
“We respect that, we get on with our work and keep developing as a team.
“It’s just natural, Man City and Liverpool are both incredible teams. We know we are looking to improve and close the gap. We have finished ninth in the last two seasons but today we looked like a top team.
“It was a real historic day, to surpass the club record of straight wins in the top flight was fantastic for us.”
Vardy, the Premier League’s top scorer with 16 goals, has netted 25 times since Rodgers’ first game in March, eight more than any other player in the top flight.
He has now struck in eight consecutive outings, three away from equalling his own Premier League record.
Rodgers added: “Jamie is such a top-level player, he is always ready when the chances come. I don’t think there’s any doubt he isn’t going to score.”
Vardy opened the scoring after 21 minutes and Iheanacho doubled the lead four minutes before the break.
Jack Grealish pulled a goal back in first-half stoppage time but Evans’ header soon restored Leicester’s two-goal advantage.
Vardy wrapped the game up with 15 minutes left while James Maddison had earlier hit the post and Tom Heaton kept the score down with saves from Caglar Soyuncu and Harvey Barnes.
Villa, who hit the crossbar through Anwar El Ghazi at 0-0, are only out of the bottom three on goal difference.
Boss Dean Smith defended the decision to keep Tyrone Mings on ahead of Vardy’s opener after the centre-back suffered a hamstring injury.
“I thought immediately he pulled his hamstring, which is why I called for Bjorn Engels,” he said.
“He’s never had a muscle injury before and the message I got was he wanted to carry on and it might have been cramp.
“He tells me he’s OK and unfortunately they score in that period.
“Goals change games. Anwar missed a chance but they had a couple before that.
“We won’t be the first or last to be beaten by Leicester. It was one of those games, Tom has kept the score down at the end. It could have ended up 8-4, such was the basketball nature of the game.”