Lennon revealed there was anger in the dressing room after the four players were announced on Wednesday following the counting of the votes from their fellow professionals.
Lennon, whose team clinched the Scottish Premier League title on Sunday, said: "It beggars belief that we make a semi-final of the League Cup, final of the Scottish Cup, win the championship, make the last 16 of Europe, beating Barcelona, beating Spartak Moscow, putting the country on the map again, and I think the outcome of those votes belittles all the efforts of the players."
No Celtic player got more support in the main category than Motherwell striker Michael Higdon, Inverness midfielder Andrew Shinnie, Hibernian forward Leigh Griffiths and Aberdeen striker Niall McGinn - who was released by Celtic last summer.
Celtic midfielder Victor Wanyama was named on the young player shortlist but Lennon viewed the democratic outcome as a snub to his side.
Lennon added: "I think it's abysmal. Are people voting for the best player in Scotland or the most improved player in Scotland?
"There's a huge difference in my eyes and that's not taking anything from the candidates that were nominated. They have all had fine seasons, but to not have one Celtic player in that group is unbelievable."
When it was put to him that the votes for Celtic players might have been spread throughout his team, Lennon said: "I have no idea what way the voting goes but you can't tell me that (Fraser) Forster, Wanyama, Kris Commons, Kelvin Wilson, Gary Hooper weren't in the forefronts of people's minds when the votes were made. It's ridiculous.
"There is a lot of ill will in the dressing room now. The players are very, very disappointed with the outcome. They have performed heroically."
- Sports & Recreation
- Scottish Premier League