Goodwillie saw his effort blocked by goalkeeper Marian Kello before he fired wide from the rebound. The striker was singled out for abuse about his off-field problems from the home fans throughout the game.
Houston said: "The question is, is that why he missed the penalty? I don't think so. I thought he played well.
"David is disappointed but he was brave enough to take the penalty and it's not the first he has missed. He has been taking some stick but he has to expect it from every fan in Scotland and he has to be big enough to take it."
Goodwillie also had a goal disallowed after two minutes, and Houston said: "According to the fourth official it was for a handball. I asked him and he said it was the referee who made the call. The referee has done well to see it from that angle but if it's a handball, it's a handball."
Meanwhile, Garry Kenneth, who limped out of the action with a knee problem and left the stadium on crutches, is set to miss three weeks after straining his medial ligaments.
Source: PA
Source: PA