No player from the SPL champions' squad, though, gathered enough votes to make the four-man short-list which includes Motherwell striker Michael Higdon, Inverness midfielder Andrew Shinnie, Hibernian forward Leigh Griffiths and Aberdeen striker Niall McGinn.
Celtic boss Neil Lennon described the situation as "abysmal" and Mulgrew, winner of the players' and the Scottish Football Writers player of the year award last season, was similarly irate. "I still don't see how one Celtic player didn't have enough votes to get into the top four," he said.
"It has been noted what we have been done in the Champions League (reaching last-16) and being so clear in the league so it's disappointing. It's baffling to be honest. What did we have to do? Did we have to win the Champions League? Did we have to win the league by 40 points? Did we have to win all the cups? I don't know? What did they expect?
"I am not saying there is an agenda but surely when people are looking at their votes they have to look at who has won the league, who is in finals and who has done well in Europe and surely everyone knows that we have done that. Surely you have to pick a player from that."
The Scotland international dismissed the notion that individual Celtic players suffered from the team being so strong as a unit.
He said: "It has been a team effort, it's always a team effort with every team, it's a team sport, that's what happens. But we have some players stand out this season.
"Kelvin Wilson has done great and Gary Hooper scored a lot of goals. The two players for me are Fraser Forster and Victor Wanyama, they have impressed me this year so you expect one of them to be in there. I don't know how other people didn't see that. I just couldn't believe it when I didn't see a Celtic player in there."
Mulgrew was also dismissive of Kilmarnock boss Kenny Shiels who, when asked about Lennon's complaints, said: "Celtic make a song and dance about everything, don't they? Paranoid FC."
"It is definitely not paranoia," said Mulgrew. "I've said how I feel about why at least one of our players should be involved in the top four. It is understandable how disappointed the manager is, everyone feels the same. The nominations are not tainted at all. They have done very well, four good players who scored a lot of good goals and deserve to be nominated."