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 ahead of the Clydesdale Bank Premier League game against Motherwell on Sunday, 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 done well in Europe and surely everyone knows that we have done that.
"Surely you have to pick a player from that."