Gary Mackay-Steven put the hosts ahead in the 52nd minute but Richard Brittain levelled eight minutes from time to leave United still without a win at Tannadice since August.
Houston said: "We needed a second goal to kill them off and, to be fair, it was a wonder strike from Brittain.
"But I can't fault the players for their attitude and commitment. It's just that the home record might be a mental thing for them.
"We played some decent stuff in the second half but sometimes these things are set to try us.
"Hopefully, though, we can mend the home record as soon as we can.
"Our away form is good but if we could just sort the home thing it would be great and make a difference."
Meanwhile, Houston is promising business as usual as the Tayside club step up their search for a new manager after he revealed recently he would be leaving in the summer.
He said: "I'm ignoring all speculation. I've declared I'm going and that gives me five months for the board of directors to find a new manager.
"So they have to get a head start on their work to ensure they get the right person.
"I'll carry on as normal. I'm contracted until May and want to get the team into Europe for the fourth season running."