The Buddies became the latest team to take something from Tannadice, where United have not won since beating Dundee in August.
Hegarty said: "Scoring three goals and coming away with nothing is disappointing.
"The goals we lost today were poor by our standards and it told in the end because we lost the three points.
"We've had too many games like that at home this year. We can't explain it."
United midfielder Willo Flood went off midway through the first half with a groin problem and the dismissal of defender Brian McLean could cause selection problems on Wednesday at Aberdeen.
Unless Sean Dillon recovers sooner than expected from a thigh injury, striker Jon Daly is likely to drop back to centre-back.
Hegarty added: "He's a quality striker and we'd rather have him up front, but we had to put Jon back (after McLean's dismissal)."