However, Tamir Cohen marked his first start of the season with the equaliser in the 59th minute.
Villa at least remain in fifth spot with Everton losing at Goodison Park to Manchester City.
O'Neill said: "In terms of the elusive win I hope it is just around the corner. Overall I have been delighted with the team and on the whole we are playing pretty well.
"We got in front before half-time which, on the balance of play, we deserved. We were in decent control in the second half, then they equalised. That is something that can always happen.
"It was disappointing to concede the goal but we have gained a point on Everton and retained fifth spot. By league table definition it means we have improved on last season.
"We have not been out of the top six all season. It is hard to break through into the top four but we gave it a go.
"There is a morsel of disappointment we could not sustain it but that is the way it happens sometimes."
Young made the breakthrough when his curler from the edge of the area evaded goalkeeper Jussi Jaaskelainen.
It was his first goal in 18 games and his last also came against Bolton in December.
Despite failing to find the target in recent months it has not affected his mood, according to O'Neill.
He said: "Ashley doesn't lack confidence. You should see him chirping around during the course of the week.
"His lack of goals is probably because he has made them all. As Stanley Matthews once said 'I cannot make them and score them at the same time'.
"Ashley has had a great season. Along with Gabby (Agbonlahor) he has done wonderfully well. They have been brilliant in a long campaign."
Bolton manager Gary Megson refuses to accept his side are safe despite moving onto 38 points.
He said: "This result helps us along the way and another win should see us stay up.
"We did okay today without playing champagne football. What we did do well was that we worked our socks off.
"I know Villa have taken the lead 13 times this season, won 11 of them and drawn two.
"Given that record we did well to get back in the game against a top-class side."
Cohen pulled them level by smashing the ball home from close range after Kevin Davies and then Andy O'Brien helped on a free-kick from Matt Taylor.
The Israel midfielder, whose progress has been hampered by injury, could not hide his delight.
Megson said: "It was a great strike and hopefully Tamir can settle down now and push on. He's had a disappointing season from his point of view."