August's victory over Russia remains the only win under O'Neill in 13 matches since he took over from Nigel Worthington, and recent defeats to Luxembourg and Azerbaijan have prompted speculation over his future.
But he is expected to be offered a contract extension by the Irish FA following their final World Cup qualifier against Israel on Tuesday, and captain Davis would be happy to see him stay.
"I think we've all enjoyed working with Michael and his staff even though results have been disappointing in the campaign," Davis said. "The frustration stems from the fact we feel we haven't got what we've deserved from games.
"I suppose I can only speak for myself but I've enjoyed working with Michael and I feel we're not far away from being a decent side.
"We feel we are on the right path and hopefully the experience gained in this campaign will stand us in good stead for the next Euros.
"We've been unlucky in a few games. We're not going to hide, results haven't been good enough, but we feel as though we're progressing."
Although fourth place in Group F is the top prize available to Northern Ireland ahead of the clash in Tel Aviv, Davis wants his side to go out with a flourish rather than a fourth successive loss.
"Without doubt we don't want to finish on a run of defeats," he added.
"We know it will be tough. Israel are a good side and a threat going forward but we want to finish on a high for ourselves and give us something looking forward.
"I'm sure they'll see the same opportunity as we do, to win the match. It should be a difficult game but a good game."