However, a much-improved second-half display resulted in Calderwood expressing his disappointment at picking up only the single point that leaves the Dons four points adrift of United in fourth and five from Hearts in third.
"I would have taken the draw at half-time," Calderwood said.
"I thought in the first 10 minutes we started really well and then we started giving the ball away and United upped the tempo and they were winning most of the tackles.
"Our passing started becoming erratic and we were on the back foot.
"Then, we nicked the goal with a dead-ball situation and we just wanted to hang on to half-time.
"We never stopped the crosses all night. We knew that was a big, big part of United's game but we never stopped them and Goodwillie got a free header.
"I've got to be honest, in the second half I thought they were wonderful and in the end you get the feeling it's two points dropped.
"We could have been blown away but I thought we did really, really well in the second half."
Calderwood was unable to shed much light on Mark Kerr's straight red card for dissent but was critical of referee Chris Boyle's display.
"I think he's a really good referee but I don't think he had his best game, I thought he was inconsistent," he added.
"Seemingly Mark said something to him. I don't know what but the referee's the boss and he decided it was a red card.
"I really do think he is a good referee but I think he had a poor game, not just because of that.
"If Mark said something he deserves to go, we know that.
"He is a big player missing for us again but I'll need to wait and see the referee's match report before I decide whether he should be disciplined."
United manager Craig Levein shared his counterpart's sentiments as he bemoaned a missed opportunity.
A victory would have sent the Tannadice side third following Hearts' defeat in the Edinburgh derby earlier on in the evening and would also have extended their lead over Aberdeen to a virtually unassailable seven points with only three games left to play.
"With Hearts losing I see it as two points dropped," Levein said. "It's a home match and at half time I felt very, very confident.
"We were shooting down the hill towards our own supporters and with the way we played in the first half I thought we would go on to win the game."