The 46-year-old joined the Foxes on a three-and-a-half year deal on Tuesday after walking out of Parkhead.
A banner was unveiled during Celtic’s 2-1 win at Hearts in midweek calling Rodgers a fraud while a video shared online showed supporters chanting abuse at their former manager.
He said: “I’ve seen what’s been said but Celtic supporters will hurt, I understand how they feel. They are hurting and maybe a little worried in terms of what might happen with me leaving.
“Words, you always have to be careful with. I’ve seen the banner, the Celtic supporters are hurting. They gave me everything so I’m not going to say anything other than that.”