Goals from Filip Djordjevic, Aleksandar Kolarov and Lazar Markovic put the game beyond Wales, who never looked like avenging the 6-1 mauling they suffered at the hands of the same opponents in Novi Sad a year ago.
Gareth Bale, a pre-match doubt due to a groin problem, appeared just before the hour to get his first action since joining Real Madrid to become the world's most expensive player.
He almost scored a wonderful late free-kick, which was about as good as it got for the hosts as they suffered their sixth defeat from eight qualifying games.
The Dragons were booed off at the final whistle, but Coleman has no intention of stepping aside, and fully expects to sign the two-year contract extension he has agreed with the Football Association of Wales.
"I have every intention of leading this side into the next qualification campaign," he said.
"We have two wins out of eight, which is not good but I am still excited about the group we could have available.
"The next campaign will be a better one."
He added: "The contract has been agreed, although I have not signed it, but if I thought I could not affect this group of players I would not waste my country's time.
"We can do something special, with a fresh run at it.
"But, as a whole, the next two or four years will be our best chance to do something with this group of players."
He added: "I am the same man as I was last week when the contract was agreed. I know football is short-term and that is how it has gone, but we did not perform tonight.
"But I am looking at the whole situation and the game, I will speak with the powers that be (about signing my contract), but I have not thought about when I will sign it.
"I know sections of the crowd weren't happy but I don't blame them."
Coleman admitted the defeat had been "soul-destroying", and that defensive errors had made Wales' task impossible.
He said: "We gave away two silly goals, and that has been the pattern of our campaign.
"We have been too naive at times, if you keep backing off sides only one thing will happen.
"The goals we gave away were poor, it's soul-destroying.
"I was excited for these two games, thinking we could get three points in Macedonia, where I fancied us, and go into this game with a strong side and Gareth playing a bigger part.
"But it was not to be and I have to take responsibility for that, I am the manager."
Coleman introduced Bale for the final 32 minutes of the game, when Wales were already 3-0 down.
And there were some eye-catching contributions from the world's most expensive player as he played his first football since his move to Real Madrid, including a superb swerving, dipping free-kick which was only just kept out by the Serbia goalkeeper.
Coleman was happy with Bale's outing, but believes he is still some way short of full fitness ahead of his potential bow for Real this weekend.
"He played 30 minutes but after 15 minutes he looked tired - but he has only had four training sessions, so you will not get what you normally get," he said.
"But he gave us a lift, the fans were excited and it gave us a spur, although the game was done and dusted.
"We needed to be in the game, it was lost by then, but it was nice for the Welsh supporters to see him."
He added: "If he starts Saturday he will not finish the game, I would be amazed if he does.
"He is nowhere near ready for 90 minutes even if Spanish football is slower.
"He may get 45 minutes, I don't know, but he will feel better in himself after 30 minutes."
Bale himself tweeted after the game: "Great to finally get back to playing tonight, shame about the result though. Can't wait to get to Madrid tomorrow #halamadrid"