The home side took the lead through a first-half Mickael Antoine-Curier spot-kick when Gavin Skelton went down in the box following a challenge from Prince Bauben.
United rallied with seven minutes to go when substitute Andis Shala headed in a Craig Conway cross for a deserved share of the spoils, but Houston felt the penalty decision was crucial.
He said: "Billy (Reid, Hamilton boss) complained last week about getting a soft penalty given against them but I will tell you what, he will not get a softer penalty than they did here.
"I thought it was very soft and the players had to overcome that and we did.
"We left it late but it should have been finished, we missed some great chances in the first half. I feel as if it is two points dropped to be honest."
Source: PA
Source: PA