The Tannadice boss was hoping his team could secure the win that would open up a seven-point gap on Aberdeen and virtually seal fourth spot in the Scottish Premier League with only three matches left in the race for European qualification.
The former Scotland defender also knew a victory, coupled with defeat for Hearts against Hibernian at Tynecastle, would have sent his side over the Edinburgh club and into third place.
However, Levein's outfit were forced to come from behind following Lee Miller's opener totally against the run of play and had young striker David Goodwillie, the match-winner against Hibs at the weekend, to thank again for rescuing a crucial draw.
United still enjoy a four-point advantage over Aberdeen and, despite the missed opportunity, Levein has been cheered by the fact they are now closer to former club Hearts, who they still have to face in the run-in.
He said: "In spite of being disappointed with the outcome, we're a point closer to Hearts - which I'm surprised at, but pleasantly surprised.
"We're still in there fighting for third. I was hoping we would have won and put Aberdeen out of the equation.
"But I'm sure they will be quite happy to pick up a point away from home and they're still in it.
"They play Hearts on Tuesday and they're still in there fighting."
With injuries ruling out John Daly and Francisco Sandaza and limiting Warren Feeney to a place on the substitutes' bench, Levein handed
Goodwillie a rare start alongside fellow-20-year-old Andis Shala.
And the Tangerines boss felt he had been vindicated in his choice of the inexperienced pair.
He added: "Goodwillie is a young boy. He's only 20 years old, although he seems to be older than that because he's been around for so long, and I thought he played well.
"With Andis Shala he looked a threat, particularly in the first half, and when you consider we had Daly, Feeney and Sandaza all not starting the match it doesn't look too bad for the future."
Aberdeen manager Jimmy Calderwood also had to deal with a selection headache going into the game, with Andrew Considine and Jamie Smith only adding themselves to a lengthy injury list 24 hours before the match.
And in the trying circumstances, which were exacerbated when defender Lee Mair had to be replaced at half-time and midfielder Mark Kerr was red-carded 14 minutes from time, the Dons boss felt his players coped admirably.
He added: "Lee Mair had a head knock and had to go off, Andrew Considine and Jamie Smith both called off after training on Wednesday and we were right down to the bare bones, so all credit to the players."