United were sunk by two first-half goals from Ryan Stevenson, and although they got back into the game via Keith Watson, the Tynecastle club held up.
"I thought the team that played the better football lost," he said.
"We played quite well in the first half as well and again it comes down to an individual error. The first goal Brian (McLean) should deal with, we didn't deal with it properly and we found ourselves a goal down.
"I haven't seen the penalty again. I thought it was a bit soft, but other people have told me it was a penalty kick.
"We found ourselves chasing the game and second half I thought we absolutely pummelled them.
"We were the away team, but we pinned Hearts back and they were desperately hanging on. They cleared everything we threw into the box, but I'm walking away from here with nothing and I feel a wee bit hard done by.
"The ball didn't break for us."