Iheanacho came off the bench with 10 minutes to go at the Etihad Stadium on Monday with Leicester trailing 1-0 to Vincent Kompany's unstoppable 25-yard strike.
The former City striker was sold by Pep Guardiola but wasted a glorious opportunity to earn the Foxes a draw, which would have left Liverpool in top spot in the table.
Iheanacho has scored a single Premier League goal this season but Rodgers felt the Nigeria international ought to have made more of his late chance.
"He should score, I said that to him afterwards, in the big games there are not many moments," Rodgers told a news conference.
"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."
Leicester were keeping City at bay until Kompany's rocket, although they posed little threat of their own, with their defeat ending any hopes of catching Wolves in seventh spot.
And Rodgers accepts it will be a challenge for Leicester to narrow the gap to the so-called 'Big Six', although it is one he is relishing following his February move from Celtic.
"It's going to be very, very difficult for us [to finish in the top six next season] but our idea is to develop the team and how we're playing," Rodgers added.
"This was an incredible counter-attacking team and what we're looking to add to that is to play a positioning game that allows you to control possession.
"I thought for large spells tonight against a really, really good side we did that. We've one more game to go, we want to finish the season as strong as we can. Then we'll put in a lot of really hard work in the summer.
"There will be other teams trying to get up there but what we've shown is we are playing with a personality and we'll only get better.
"The Premier League is the greatest football stage in the world, every club I've went to there has been a challenge of some sort.
"To come into Leicester, where Claude [Puel] had done a very good job before me, you had the real sadness of losing [chairman] Vichai [Srivaddhanaprabha] earlier in the season.
"But I look at the squad, the potential in the squad, a lot of young players that I believe can develop and can improve. To come into games like this here and nights like this is what the Premier League is about.
"It's a great challenge against guys that are geniuses like Pep and the other great coaches. Pit your wits against them. That's the challenge as a professional coach."