O'Neill's side salvaged a 1-1 draw against Israel in Tel Aviv, a highly creditable result given a number of experienced absentees including Jonny Evans, Gareth McAuley and Aaron Hughes.
The visitors had gone behind just before half-time to Eden Ben Basat's headed effort and looked to be on course for a fourth straight loss.
But Davis made sure that would not be the case when he raced on to Jamie Ward's square pass and lashed home with 18 minutes left.
It was the Southampton midfielder's first goal of the campaign and his first since being handed the armband by O'Neill.
"If you wanted to criticise Steven you could only say he doesn't chip in with enough goals because his overall quality of play is excellent," said the manager.
"We tried to play him a bit higher up the field and it was a good piece of play and a great finish.
"It's difficult to be a manager when you're not winning games but it's not easy being the captain either and he's handled himself very well.
"I'm delighted for Steven."
O'Neill's contract expires at the end of the year and he currently has no more games in the diary.
But talks with the Irish Football Association will resume later this month and he will approach them with a reminder about the transitional work he has had to undergo so far.
"We'll deal with all that when it comes along, but the bottom line is this group of player is still developing," he said.
"This result was a positive at the end of a few negatives but we have to look back on the group as a whole and know we could have done better than we could have.
"Probably 60 per cent of the squad are in their first real campaign, having their first real experiences of playing in these kind of venues and playing for what is at stake here.
"We can only be better as a group for that."
O'Neill was particularly pleased with the performances of those he drafted into the side after defeat in Azerbaijan last week.
With suspensions thinning out the options in defence Bradford's Rory McArdle was handed a first competitive start, with Chris Baird and Sammy Clingan recalled to the midfield to provide experienced support.
"We're here without the likes of (Aaron) Hughes, Evans, McAuley and (Oliver) Norwood but the players who came in were excellent," said O'Neill.
"McArdle did a great job and Chris and Sammy were excellent in the middle of the park as well. I thought we managed the game well.
"After 75 minutes of every game in this group the result has been in balance and too often we've come out on the wrong side of the result.
"Sometimes that has been our own fault and sometimes there's been elements of misfortune. But I think tonight a draw was the least we deserved given the way we performed in the second half."