Two second-half goals from Marvin Sordell (below) sent the Championship side through to an FA Cup fourth round clash with Everton and left O'Neill to look ahead to a gruelling battle to secure his side's top-flight future.
O'Neill said: "The fact it is 40 years since we've won a trophy is far too long. We enjoyed a really good run last season and put some big results together in January and February, then we played Everton and were disappointing -- but that was a quarter-final.
Here we had the opportunity to play Everton again and we didn't take it . We're going to have to get it (consistency). This is a big club and we shouldn't be spending 40 years without winning something, we really shouldn't."
O'Neill named his strongest available side, including James McClean, for the Stadium of Light replay in contrast to his Bolton counterpart Dougie Freedman, who made six changes from his side's draw with Millwall.
A delighted Freedman said: "We're looking forward to it (Everton). We feel right now that we can perform against anyone, and if we defend like we did and keep our discipline, we have definitely got every chance."