But the national team boss claims he has also taken plenty of encouragement from the stalemate as they began their World Cup campaign with a point.
The Scots had been hoping for maximum points from two home games against the Serbs and Macedonia to give them the best possible start in what is set to be a tough Group A.
Although disappointed by the result, Levein refused to be too down at the outcome of what he always expected to be a tough opening qualifier.
"It was going to be difficult to get a victory today, we acknowledged that and we didn't manage to get the three points," he said.
"I'm disappointed but more about the fact that we had opportunities and didn't take them.
"The upside for me is that we had a number of players today who, although they played well, can play an awful lot better so there is encouragement as well.
"Nothing has changed. In fact, I'm more confident now than I was before the match.
"I'm disappointed we didn't win but I saw the chances we created, I look at the opportunities we had to hit Serbia in the areas where we knew they were weak and I could count half a dozen times when we just didn't play almost a simple pass to put people through on goal.
"That won't happen again. Our guys will improve in that regard and that gives me encouragement that we're going to be better on Tuesday."
Asked if Tuesday's game against Macedonia is now one the Scots need to win, Levein replied:
"Probably, yes. Certainly it would be beneficial to win the game on Tuesday.
"We wanted to win today as well and we did enough to win the game, we just didn't score the goals. That's football.
"We have played teams of a similar standard to Serbia before and didn't have enough possession and chances.
"We have moved forward enormously in that regard. I see a huge progression.
"I'm disappointed but I'm not down about it. The lads put on a decent show today. I thought we deserved to win the game.
"The over-riding feeling is disappointment but it's a point, it's us off to a start, and it's an opportunity to look to Tuesday and try to take it up to four points."
"You can't go back over and over the chances and wish they had gone in. That's done.
"Our lads proved today, without firing on all cylinders, there is more to come. We've got a decent chance of improving as things go on."
Levein threw James Forrest into the action with 20 minutes to go but waited until the final 10 minutes to introduce Jordan Rhodes and James Mackie.
Asked if there was a temptation to make those changes earlier in the game, the manager said:
"There was. I made the change of putting James Forrest on just to open things up.
"I was hoping to get an instant impact.
"I thought James was excellent when he went on but it was a slow burner and it took him a little while to get into the game.
"It's easy now that the game is finished. I might have put the three on at once but sometimes it happens for you and sometimes it doesn't."
Levein has yet to decide whether he will make changes to personnel for the visit of Macedonia but is pleased by the options he has at his disposal.
"The good thing is that there's competition for places," he said.
"Jamie Mackie went on and made a huge impact on the game, James Forrest went on and made a huge impact and Jordan was a yard away from the ball bouncing kinder to tap one in.
"I think it's encouraging. It's an unusual situation for me to have so many good players who can come on the field in this international game so that was hugely encouraging as well."
There was a suggestion that Steven Naismith may have elbowed Srdan Mijailovic in an off-the-ball incident.
But Serbia boss Sinisa Mihajlovic refused to be drawn too much on the incident, saying only: "This is football, not ballet."
He had been hopeful of leaving Glasgow with a win but was satisfied with a point.
"I would say that 0-0 is more or less an honest result," he added.
"I expected honestly that we would win against Scotland but we made a few mistakes.
"Scotland had some chances in the first half and also two or three in the second half.
"I must be satisfied with the point at the start of this qualification round, although we have some things to change to be better in forthcoming matches.
"If you cannot win, it's important not to lose."
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