Kris Boyd had given the Gers a half-time lead but United hit two goals in four second half minutes, both from crosses, to nudge in front.
"I feel that we should have taken advantage of the situation where we played very well in the first half," Rangers boss Walter Smith said.
"When we didn't, we knew there would be a response from United at the start of the second half.
"I am disappointed with the level of goal we lost. They were simple, bread-and-butter crosses we should have dealt with.
"But credit to the players for the way they came back. United had the ascendancy for the first 15 minutes of the second half but we came back stronger.
"Without having any clear-cut chances, we looked like we could have got the winner."
"The situation is of our own making," Smith said.
"It's not as if, away from home, teams have been pinning us back.
"We have had most of the territorial advantage and most of the possession in games and haven't managed to win them.
"Plus the fact we have given away easy goals, which we haven't done at home. It's something we have to look at and make sure we cut it out.
"Our overall performances have been good - except for Hearts where we didn't really create anything.
"I don't think we need to make drastic changes. We definitely need to toughen up a bit, especially away from home."