Both managers agreed Everton were fortunate with their penalty in yesterday's 1-1 draw against Sunderland.
Ref Howard Webb 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 Martin 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.
"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.""I did speak to Howard. He hadn't seen it back - I obviously have had the advantage of seeing the incident back.