Iheanacho missed a gilt-edged chance to equalise against City on Monday after Vincent Kompany’s title-defining opener.
The 22-year-old, who spent three years at City before leaving for Leicester in 2017, missed when put through on goal in the closing stages.
Rodgers says he told Iheanacho that he should have scored after the game.
“It was the best chance in the game, and he’s disappointed in the changing room,” he said.
“He should score, I said that to him afterwards, in the big games there are not many moments.
“It was tight, we were very, very good in our defensive organisations. They didn’t have many chances and we didn’t have many. But the one that came, you have to score that. He knows.
“It’s moments when you can come into the game and make an impact, he’s a great boy, works very, very hard in training.
“He’s got in front of him a top-class operator in Jamie [Vardy] so it’s difficult for him to find rhythm. However, it’s moments like that where you can make an impact. He’s actually done that in the other games.
“It was a big chance for him, the ball was there and it was on his good side. But it wasn’t to be. He got himself in the position, I felt we would have deserved that at least.”