The former Manchester United boss, who retired at the end of last season, stated in his book My Autobiography that Henderson could have fitness problems in the future because of his running style.
"The one thing that I will add that I was disappointed about, bitterly disappointed about, was what he said on Jordan Henderson," Rodgers said in a press conference. "Sir Alex is obviously someone who works with young players and nurtured them.
"The statement in terms of Jordan was inappropriate really. This is a young guy who I've worked with now for over a season, and you won't get a more honest player.
"So I'm sure that, somewhere along the line, if Sir Alex bumps into Jordan Henderson he'll apologise for that because it was something I didn't think was right, especially from someone who knows that every word to a young player is important."