Three team-mates have made the shortlist - Stuart Armstrong, Moussa Dembele and Scott Sinclair - along with Aberdeen winger Johnny Hayes.
But Rodgers feels his captain should not have been overlooked.
"I still can't get away from how Scott Brown's not on it. I really can't," he said of the Scotland midfielder.
"I don't know what he was like in other years, but for this season, in my first season up here in Scotland, the level that this man has played at, he's the most influential player in Scottish football.
"I look at Chelsea's N'Golo Kante down south as a central midfield player and I think he got the player of the year award down there - and I think that Scott is certainly at least worthy of being a nominee."
Rodgers, though, would not reveal whether 31-year-old Brown would have been his choice for player of the year.
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He also declined to nominate which of the three Celtic players on the list deserved to win.
However, he praised the consistency and leadership shown by Brown throughout the campaign.
"I can only remember him having one bad game and that was Hearts when we won the league - and I think he said it himself he was hopeless," added the Rodgers.
"Every other game 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. He has been superb.
"I can't believe why he isn't in it, but of course, I'm really happy for the other boys and the young players that are nominated as well."
At Ibrox on Sunday, Sinclair was subjected to racial gestures from a Rangers fan, who has since admitted the offence in court, and Rodgers said the English winger had put the incident behind him.
"Racism - whether it is football or whether it is society - there is no place for it," added Rodgers.
"He's fine. He's got the support of all the people here, all the supporters and he moves on from it.
"He's been playing the game quite a long time, so it says something that it's the first time he has come across it in his life.
"There's been so much great work over the last 20 years to wipe out this kind of thing.
"In this day and age, when you do hear about it, it's very, very surprising, so thankfully it's been dealt with straight away, which is good to see, and we hope we don't have any more incidents like it for players like Scotty and whoever else."

He was due to open in the Arthur Miller play Death of a Salesman at the Royal & Derngate in Northampton on 10 April, but died three days beforehand.
The theatre said the role of Willy Loman would now be taken by TV and film actor Nicholas Woodeson.
Shows in Northampton have been postponed and the play will now open in Cambridge in May, ahead of a UK tour.
Pigott-Smith died at the age of 70, a month after collecting an OBE for services to drama.
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He had been rehearsing the role of Willy Loman in Miller's play which was expected to open at the Northampton theatre ahead of a tour including Cambridge, Bath, Exeter, Edinburgh and Oxford.
A spokesman for the Royal & Derngate said the decision to proceed with the production and tour of Death Of A Salesman was made after consulting the "acting company, creative team and touring partners".
Pigott-Smith's replacement, Woodeson, is well-known for roles in a number of dramas including Taboo, The Living and the Dead, Rome, Mapp and Lucia, and also for film roles including in the Bond movie Skyfall.
The play will now open at Cambridge Arts Theatre on 4 May.
Ticket-holders for the postponed run in Northampton would be offered a refund, or tickets for the rescheduled run at the Royal & Derngate at the end of the tour, organisers said.
Celtic manager Brendan Rodgers cannot believe Scott Brown is absent from the nomination list for the PFA Scotland player of the year award.
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Theatre directors have confirmed a show will go on despite the death of its star, the actor Tim Pigott-Smith.