It was suggested that the Northern Irishman had offered to quit his position after seeing his side lose at home for their third defeat in four games in the Premier League, leaving them three points above the relegation zone.
But the club have told Sky Sports that O'Neill has "unequivocally not resigned" and will not leave Wearside in the wake of their latest match.
|A REASON TO STAY|
|5/4||Sunderland are 5/4 with William Hill to beat QPR on Tuesday night|
O'Neill remained upbeat despite the defeat to Steve Clarke's high-flying side, insisting that he was pleased with his side's second-half performance after they fell behind in the first 45 minutes.
"The second goal makes it a tough task but we fought back terrifically and I thought we were going to force the equaliser first time round at 2-2 and of course the penalty decision goes against us," O'Neill told the BBC.
"I was very pleased with the second-half performance, delighted with it. They're probably as good a counter-attacking side outside the top sides and are up there on merit."