The absence of Celtic players from the four-man short-list, which includes Hibs striker Leigh Griffiths, Motherwell forward Michael Higdon, Inverness midfielder Andrew Shinnie and Aberdeen frontman Niall McGinn, has not gone down well at Parkhead.
Hoops boss Neil Lennon described the outcome of the vote as "abysmal" while Celtic defender Charlie Mulgrew, who won it last year, called it baffling, even though seven Hoops players received nominations from their fellow professionals with midfielder Victor Wanyama up for the young player award.
Kilmarnock boss Kenny Shiels stoked the furore when asked about Lennon's complaints, saying: "Celtic make a song and dance about everything, don't they? Paranoid FC."
Stevenson, ahead of Saturday's Clydesdale Bank Premier League clash with St Mirren at Easter Road, where one point will keep the Buddies safe from relegation at the expense of Dundee, insists he keeps an open mind when casting his vote.
"I'm sure I did vote for a Celtic player," he said. "I think I voted Wanyama and Higdon - you get two choices - and I'm sure I voted Wanyama for young player.
"If a Hearts player was a stand-out I would have no problem voting for him.
"It would be hard for me to vote for a Hearts player but he is a professional player and you wouldn't vote against him because he is a Hearts player.
"It was hard to pick a Celtic player because there are a lot of them that good, it is hard to single any of them out.
"But you can see why Leigh has been voted. He has stood out head and shoulders above the rest of us, him and Ben Williams. I'm sure Ben has the chance of being in the team of the year."
- Sports & Recreation
- Leigh Griffiths
- Victor Wanyama
- Neil Lennon
- Michael Higdon
- Andrew Shinnie