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."
Source: PA
Source: PA