Allardyce fumes at penalty decision
Adam Johnson went to ground in the area under minimal contact from James Tomkins in the 22nd minute, with referee Phil Dowd pointing to the spot.
Jordi Gomez stepped up to convert the spot-kick and hand Sunderland the lead, and Allardyce was fortunate not to be sent to the stands after voicing his bemusement at the decision to Dowd.
The West Ham boss remained adamant that the officials made the wrong decision at his post-match media conference.
"It's a dive," he said. "I've seen four angles on the laptop and the assistant referee has made the wrong decision in my opinion.
"It wasn't the referee's decision because he couldn't see from where he was.
"Out of all the experience he's gained over the years, if he doesn't see that that's a dive that's concerning, I have to say.
"Johnno knew he was going nowhere, he knew the ball was going out of play, so he thought: 'Well, I'll have a little fall down so the referee has to make a decision'. And it went in his favour."
Stewart Downing pulled West Ham level seven minutes later, and Allardyce insisted he was content with a draw under the circumstances.
"I think you're always happy with a point away from home," he added. "In this division, playing away from home is never an easy task, wherever you go.
"To recover from the poor decision on the penalty shows good character.
"It's the third time we've had to come from behind in the last three games.
"Even before the penalty, I thought we were unlucky not to score.
"A good point in the end. We went all out to get three, couldn't quite manage it, but I was satisfied with a point."
The result brought to an end West Ham's three-match winning run.