But the national team boss claims he has also taken plenty of encouragement from the stalemate as his side began its FIFA World Cup campaign with a point.
The Scots had been hoping for maximum points from two home games against the Serbs and FYR
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.
He said: "It was going to be difficult to get a victory today, we acknowledged that and we didn't manage to get the three points.
"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
"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."
He added: "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."
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
"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
He said: "The good thing is that there's competition for places.
"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."
Neil Lennon believes some Scotland players "need to leave their egos at the door" if the national team is to emerge from its current slump.