Winston Reid snatched a 1-0 victory for the hosts with the last kick of the match, a shot from the edge of the box through a crowd of players
But Black Cats boss Moyes felt Hammers substitute Jonathan Calleri was in an offside position - and in goalkeeper Jordan Pickford's line of sight - as the ball flew past.
However, referee Bobby Madley gave the goal and rock-bottom Sunderland were consigned to a seventh defeat from nine matches this season.
Moyes said: "The match official thinks it's onside, I definitely think it's offside.
"You could tell by his reaction, he walked towards the linesman, so he was aware there was a problem with it.
"That's what the disappointing thing is
The players earned something from this game, it might not have been pretty but we are trying to build confidence.
"We should have dealt better with the corner but we still needed a decision to go our way, and it didn't go our way."
The goal was certainly harsh on Sunderland, who after somehow surviving a Dimitri Payet onslaught for the opening half an hour looked like holding out for a point
Sunderland simply could not handle the France midfielder in the opening stages
Payet curled one shot inches wide, crashed another against a post and went on a mazy run past four defenders into the area only to be denied another goal-of-the-season contender by Pickford
Yet as West Ham - and the crowd at the London Stadium - became more frustrated, the Black Cats were on course for a valuable point and a first clean sheet of the season
That was until Payet took a short corner, received the ball back and squared it to Reid, who in one fluid movement turned and arrowed a low shot into the net
What centre-half Reid was doing on the edge of the area, rather than inside the box waiting for a cross, not even manager Slaven Bilic could explain
"That certainly was not one from the training ground," Bilic admitted
"Sunderland made a mistake, they thought we would put the ball into the six-yard box - but then so did I!
"But it was a great decision from Payet and Mark Noble to bring the ball outside the box and play it to Reidy
If his shot is blocked you'd say, 'Why didn't you cross it?' but it turned into a great decision from the players
"Of course you have to be a bit lucky to score that goal, but it was crucial
It was very dramatic and in a very important game for both teams."
Source : PA
Source: PA