Jamie Vardy gave his side the lead in the first period but the second period belonged to Moss dismissing Vardy before awarding a penalty to the visitors for Andy Carroll to equalise.
Aaron Cresswell looked to have snatched all three points but Moss pointed to the spot once again deep into extra-time for Leonardo Ulloa to retain a point for the champions elect.
It seemed to be a small offence in the favour of Claudio Ranieri's side when a soft push from Carroll sent Jeffrey Schlupp to ground but despite his frustration, Bilic offered sympathy for situation that Moss was put in.
He told Sky Sports that they team were "gutted" and felt that they had done "enough to win the game".
He continued saying that is was "hard for the referee" as "every ground" would shout for "handball and a foul" and that he did "feel for him a little" but ultimately he thought it was "not a penalty" but it was the "pressure and situation" that made it "hard for him".
Still in the race
Despite that minor setback, West Ham are still in contention to finish inside the top four with their chances been boosted by Arsenal's 1-1 draw with Crystal Palace later that afternoon.
Seven points is currently the difference but Bilic admitted that the way his side came from a goal behind was positive.
He said that his side showed "character and quality" and even when Vardy struck home in the first half his side "didn't lose shape"
He continued saying that his side "coped well" with the Foxes' counter attacks in the second half and admitted that the draw was a "big frustration" as he felt that his side "deserved to win the game".
West Ham United will host Watford at the Boleyn Ground on Wednesday, April 20 with kick-off at 7:45pm BST