A distressing evening at Goodison Park saw a lowly Everton side dominate and bully Wolves with four goals from set pieces.
It is one of the lowest ebbs in a difficult season as pressure mounts on O'Neil.
Travelling supporters called for his sacking, but O'Neil has faith that he can turn around the club's fortunes.
O'Neil said: "I will back myself in any role given to get the most out of the group that we have. In any role.
"I understand the drive for change from the supporters. You never know how many of them it is and what percentage it is. The negative noise is normally the loudest.