Steven Fletcher's fourth goal in three matches had put Sunderland ahead and West Ham dominated the game without reward until 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."
Nolan had an acrobatic volley saved brilliantly by Mignolet and missed another effort from close range while Carlton Cole, Ricardo Vaz Te and James Collins all squandered good chances.
"Sunderland had four attempts at goal today. That shows the dominance we created but our Achilles heel was our finishing," Allardyce added.
"It wasn't good enough and that made us struggle to the very end. From a manager's point of view I have to be concerned about that."
Fletcher had taken advantage of a mis-hit pass from Collins to put Sunderland ahead after nine minutes.
After that, the Black Cats were under siege but could still have put the game to bed with chances on the counter-attack wasted by David Vaughan and James McClean.
In the end, Sunderland had to settle for a fourth consecutive Premier League draw.
"I am obviously disappointed," manager Martin O'Neill said. "We looked as if we had dealt with just about everything that had been thrown at us but we were never able to kill the game off.
"We had some great opportunities in the second half. West Ham were pressing forward and leaving the door open for us. We should have taken advantage of it. We should have won the game.
"Fletcher is playing brilliantly for us. He has scored all of our goals so far.
"He is bringing players into play, he is proving himself an all-round high quality centre forward."