Gernot Rohr had left the Leicester City striker out of his squad that tackled Seychelles and Egypt after a poor showing against South Africa last year.
The Super Eagles coach advised Iheanacho to become more “serious” and “professional”.
However, his coach at club level, Rodgers said: “When I saw him at Manchester City, he was always a young player that could come in and affect the game.”
“Then he’s come here with a big price-tag.
“From what I’ve seen in training and when I’ve spoken to him, he has shown a wonderful appetite and enthusiasm to get better.
“We have a culture where we want to improve players and make them better and he’s responded very well to that,” Rodgers said on Friday ahead of their Bournemouth fixture.