The official awarded a penalty after Leon Osman went to ground in the box six minutes into the second half, although television replays showed there had been no contact with any Black Cats player.
Leighton Baines scored from the spot to cancel out Jack Colback's first-half opener, but O'Neill was quick to seek out Webb after the final whistle.
He said: "It's not a great decision by an otherwise top referee.
"I did speak to Howard. He hadn't seen it back - I obviously have had the advantage of seeing the incident back.
"Naturally, he must have thought there was contact. Clearly, there wasn't and it's obviously disappointing."
Everton counterpart David Moyes was in complete agreement with O'Neill, although he admitted he initially thought it was a penalty.
He said: "I did, yes, but I've had the chance to see it again. I don't think it's a penalty kick - well, it's not a penalty kick.
"It's a terrible decision by the referee. It wasn't a penalty kick and Martin should feel hard done by."
However, O'Neill was conciliatory as he reflected upon a missed opportunity for a third win in the first four games on his reign on Wearside.
Asked if he had missed referees during his 16 months out of the game, he said with a smile: "I think I probably did, you know, I think I probably did.
"I have to preface everything - I even said this to Howard - by saying the job they do is the most difficult in the business.
"He was seven or eight yards away, he only get one look at it. It's a difficult task, but I think I did miss them."
Having started in uncertain fashion as Everton squandered a series of fine chances to open the scoring, Sunderland took the lead with 26 minutes gone as substitute Colback made a swift impact.
The midfielder, who had replaced injured defender Titus Bramble five minutes earlier, was perfectly positioned to benefit from Stephane Sessegnon's jinking run and saw his shot deflected past keeper Tim Howard for his first senior goal for the club.
However, Everton, who have not lost on Wearside for a decade and have now gone 15 games against the Black Cats without defeat, extended their run with 51 minutes gone.
Osman perhaps should not have been allowed to make his way into the penalty area unchallenged, but as Wes Brown and Lee Cattermole closed, he went to ground and Webb, having taken his time, pointed to the spot.
Television replays suggested the midfielder had simply kicked the ground, but Baines took no notice of the fury around him to smash the ball high to Keiren Westwood's left and claim a point.
Moyes was happy enough with a point having feared the chances which went begging early in the game might prove costly.
He said: "We played really well for 25, 30 minutes and we had two great chances - Tim Cahill was through and Louis Saha had a header at the back post.
"We played really well and were the better team, but we couldn't capitalise to score our goals and Sunderland grew into the game.
"It ended up as an own goal - it was going into the goalie's arms, the shot, but took a deflection and went in."