O'Neill is fighting for his job after a disastrous five days which has seen Wolves concede eight goals.
After shipping four goals at home to Bournemouth on Saturday, the club are now 19th in the Premier League and three points from safety after another calamitous display, this time against Everton.
As O'Neil walked over to console his players at full-time, the Wolves fans were heard furiously jeering their under-fire boss.
Crowd footage shows the travelling faithful chanting 'sacked in the morning' at their own boss.
It was the fourth time this season that Wolves have conceded four goals or more in one game - and it is not even January.
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In 14 matches, O'Neil's men have shipped an astonishing 36 goals, more than any other team - and talkSPORT understands the Englishman is under increasing pressure at board level.
While the current plan is for O'Neil to remain in charge for Monday's game at home to West Ham, the hierarchy are aware he has lost the support of many match-going fans.
Sources close to the former Bournemouth boss fear he is running our of time to change the club's fortunes around after winning just two top-flight matches this season.
Reacting to criticism from the fans, O'Neil said: "Whatever the fans think of me, there is definitely no-none working harder than me and I will continue to do so until someone tells me not to.
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"I go over there to see them because I appreciate every one of the Wolves fans. They have given me unbelievable support since I arrived at the football club.
"We managed to produce some unbelievable stuff last season with a team that was heavily tipped by most of the nation for relegation. We managed to enjoy it together.
"Now it is tough. I was happy to go over there and look them right in the face and take any criticism they want to throw at me.
"I accept responsibility for my part in that. Whatever criticism they want to throw at me will not change how I feel about them.
"Everyone at this football club needs to do more. We will get back to be ready to fight again on Monday.
"I will work with everything I have. I will back myself to get the most out of the group. I understand the drive for change (but) you never know how much of a percentage of supporters it is."
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