O'Neill lauds match-winner Lafferty
The Norwich City player was a nuisance throughout and made a telling difference in the latter stages, claiming an assist for Niall McGinn's close-range effort before netting the winner with two minutes to spare.
Tamas Priskin had given the hosts the lead in Budapest, nodding in with 15 minutes to go, but Northern Ireland fought back brilliantly to end an eight-game winless run with a 2-1 triumph.
Lafferty's goal secured only Northern Ireland's second win since O'Neill took charge in December 2011 and the coach was delighted to have the former Palermo forward available once again.
"Kyle came up trumps, giving a big performance for the 90 minutes," he told Sky Sports.
"Kyle knows how important he is to us. We've not had him available to us enough, but when you see him like tonight; focused and energised, he gives a lot to the team.
"And there were a lot of big performances throughout the team tonight. [Steven] Davis and [Chris] Baird were magnificent in the midfield and Conor McLaughlin was outstanding at right-back.
"I knew and believed that we were capable of coming here and getting a result.
"When you lose the goal and in the nature we did I feared the worst at that time. I didn't think it was deserved.
"It happened at a time we lost Gareth McAuley who is obviously a big presence at set pieces. I felt the only way we'd lose a goal was from a set-piece. But the reaction to that was most pleasing."
Northern Ireland have never reached the European Championship finals and have not played in a major competition since the 1986 World Cup in Mexico.
However, the win in Budapest reaffirmed O'Neill's belief that his side are capable of challenging the likes of Greece, Romania, Finland and the Hungarians for a top-three spot in Group F.
"It enhances my belief that we can compete in this group," he added. "It's always difficult to not get carried away with one result, but that's all it is.
"We have a home game against the Faroe Islands next so these three points are only valuable if we pick up three points against the Faroes.
"But it’s a great start, the players needed that boost and the players will have enjoyed the experience of being here. Hopefully we can carry this on throughout the campaign."