The 1-0 loss, courtesy of Aleksandar Kolarov's second-half strike, pushed Ireland down to third place in Group D, with Wales's 2-0 win in Moldova lifting them up to second.
Ireland face Moldova in Dublin next month before concluding their campaign against Wales in Cardiff and even two wins would not guarantee them a place in the play-offs.
But O'Neill, who guided Ireland through the play-offs to the Euro 2016 finals, was in confident mood despite the first home defeat of his Ireland tenure.
"Absolutely not," he said, when asked if the defeat spelled the end of Ireland's chances. "We can win our last two games, we can still make it. No doubt, I'm very confident we can win both games.
"I said that to the players in the dressing room. Obviously, we've a lot of disappointed players after that performance but it's not big words from me, it's how I feel. I think we can win both games."
Ireland were more impressive than they had been in drawing 1-1 against Georgia at the weekend but failed to seriously trouble Vladimir Stojkovic in the Serbia goal.
Daryl Murphy, who disrupted the Serbian defence when he came off the bench late on, had a penalty claim but referee Cuneyt Cakir waved the appeals away.
"I didn't see it but the players are adamant it was a penalty kick. They said it was clear-cut," O'Neill said. "The referee has chosen not to give it.
"But listen, I thought the players were fantastic, they gave every ounce for the shirt, every single ounce, they'd nothing left. It was a big, big effort. It would have been the least we deserved if we'd gotten the penalty and converted. I don't remember them threatening us.
"We need to beat Moldova and Wales now, and had you told me at the start of qualifying that we'd need to win the last two games, one at home, one in Cardiff, I'd definitely have taken it."
Serbia boss Slavoljub Muslin, who now has one foot in Russia with games against Austria and Georgia to come, was delighted with his side's battling performance.
Nikola Maksimovic was sent off in the 68th minute, while full back Jagos Vukovic was injured and playing in attack for the final minutes, but the visitors held on to hand Ireland their first competitive defeat at home since 2013.
"I asked my team to play our game. We were lucky to score the goal, and in the end we played a little less successful 15 minutes because we had a player less left on the pitch," Muslin said.
"I must congratulate my players, they fought very hard," he added.
