The Parkhead side have Scott Sinclair, Moussa Dembele and Stuart Armstrong on the shortlist along with Aberdeen winger Jonny Hayes.
Dembele is also among three Celtic nominees in the young player category along with Kieran Tierney, Patrick Roberts and Hibernian striker Jason Cummings.
Celtic manager Rodgers made comparisons with Chelsea midfielder N’golo Kante as he expressed puzzlement of the omission of “the most influential player in Scottish football.”
He said: “There is a real happiness for those players because of all of them who have been nominated have been absolutely first class through out the season.
“They have really shown their professionalism and quality. So it is nice for them to be recognised by their fellow professionals.
“I still can’t get away from how Scott Brown is not on it, I really can’t. I don’t know what he was like in other years but for this season, my first season in Scotland, the level that this man has played at.
“I said it a few weeks ago, he is the most influential player in Scottish football.
“I look at Kante down south as a central midfield player and I think he got the player of the year award down there and I certainly think that Scott Brown is worthy of at least being a nominee.
“So I found it incredible, really, that a player who has played at the very highest level from the first game (isn’t nominated).
“I can only remember him having one bad game since I have been up here and that was Hearts when we won the league and he said it himself that he was hopeless.
“Every other game he has been at a top level and this is Champions League, this is big games.
“The players here will tell you the catalyst he is for them, what he gives the team and in every facet of the game he has been absolutely superb.
“So I cant believe why he would not be in it but as I say two-fold, I am really happy for the players nominated.”