Hamilton head coach Brian Rice could not believe his side failed to take anything from what he felt was their best performance of the season.
The home side had 27 efforts at goal but could not find the finishing touch as they fell two points behind Kilmarnock and three behind Ross County in the Scottish Premiership.
Rice said: "I can't believe we didn't win the game never mind draw it. That's the best we have played this season by a long way.
"When you have that much possession and playing as well as I thought we were playing, and creating chances, you expect one to go in. But it was just one of those days, it didn't go in and we made a mistake at the other end and got punished for it.
"Dundee United have done a job on us but I can't be any prouder of my players with the way they played. It was an absolutely phenomenal response to going a goal behind."
United moved into seventh place and removed any lingering doubt about their top-flight status.
Manager Micky Mellon said: "A great win, another clean sheet, the first time we have won on 4G for a long time.
"So pleased about that and pleased we now know we are going to play in the Scottish Premiership next season after just coming up.
"I would have liked to have seen us better with the football and build a bit better. We are better than what we showed at times technically but we created a lot of chances and could have made the afternoon a bit more comfortable for ourselves.
"But it's a valuable three points on the road. They are finding ways of winning now even when we don't play in the style we want to get at times."
A week after Rice's angry post-match complaints about penalty decisions, there were three strong claims rejected by Bobby Madden, two from Accies.
Bruce Anderson went down after checking inside Mark Reynolds before Mellon called "stonewaller" when Hakeem Odoffin slid in on Louis Appere. And Scott McMann felt he was pushed by Peter Pawlett in stoppage-time.
When quizzed on whether his side should have had a penalty, Rice said: "I don't know, I have not seen it. Listen, I am not talking about referees and not talking about penalties. I said enough last week, I got it off my chest last week just to let you know we are not going to roll over and be tickled by anybody.
"Bobby Madden is a good referee and Bobby called it the way he saw it. I have no qualms about today."
On United's penalty claim, Mellon said: "I don't think there was a person in the stadium who felt it wasn't.
"We, like everybody else who is shouting and bawling, maybe we don't get many penalties either. You just get used to it and get on with it and try to win games of football.
"I just couldn't believe it but I don't want to be talking about penalties."