Lennon believes the effort his players put into domestic and European competition this season has been completely overlooked.
Fraser Forster and Victor Wanyama received accolades for their displays in helping Celtic reach the Champions League last 16, while Kris Commons has been instrumental in helping the team retain the SPL title and reaching the Scottish Cup final.
Lennon also revealed his players were perplexed at the lack of recognition by their fellow professionals who named Leigh Griffiths (Hibs), Andrew Shinnie (Inverness), Niall McGinn (Aberdeen) and Michael Higdon (Motherwell) as their four candidates.
"It beggars belief," he said. "We make the semi-final of the League Cup, the final of Scottish Cup, win the Championship and make the last 16 in Europe.
"We are putting the country on the map again, and the outcome of the votes belittles the efforts of players. It's abysmal.
"Are people voting for the best player or most improved? I'm not taking away anything from the candidates, they've all had fine seasons, but to have no Celtic players in that top group is unbelievable.
"After the outcome yesterday there is a lot of ill will in the dressing room. I am very disappointed none of my players have been recognised.
"For all their efforts in putting Scottish football back on the map in a positive way, it's a smack in the face. There was a lot of anger and bewilderment and I totally understand that."