Steven Fletcher's fourth goal in three matches had put Sunderland ahead and West Ham dominated the game without reward until Kevin Nolan beat goalkeeper Simon Mignolet with a shot on the turn in the dying seconds.
"Didn't we deserve more than that on the balance of play? I thought from the start to finish we were the dominant side and created far more chances," Allardyce said.
"Because we didn't capitalise by having enough players showing a clinical finish we have ended up having to be satisfied with a draw.
"We are relieved and happy to have a point because, irrespective of who was the better side, we were still 1-0 down.
"But we will wake up tomorrow disappointed, knowing we should have won the game on the chances we created.
"At that late stage the point is something we are happy with but overall we are disappointed."