United went ahead through defender Gavin Gunning's second-minute header and looked to be on course for a first SPL home win since August.
But Brian McLean's own goal two minutes after the break proved enough to earn Steve Lomas' Saints side a point.
It left Houston bemoaning United's inability to close out matches once ahead.
"It was a very open entertaining game for the supporters but it's hard work being Dundee United manager," said Houston.
"I think we're playing some really good stuff and we're attack-minded but, in the same breath, we're not killing teams off.
"Gavin Gunning could have had a hat-trick of headers in the first-half. Rudi Skacel had a chance as well which was cleared off the line while at the same time Radoslaw Cierzniak had some good saves as well.
"I felt with the chances we had we could have been comfortably ahead at half-time. St Johnstone, to their credit, came out spirited in the second-half and got the goal quickly.
"Gavin thought it was going out for a goal-kick but Brian was unfortunate to turn it into his own net.
"It was game where we were hoping to start a run of home wins but it wasn't to be and we're disappointed to get just the one point."