A comedy of errors inside the first five minutes allowed Rory McKenzie and Borja Perez to claim their first goals for Killie before Jude Winchester grabbed the hosts' third inside 10 minutes to give Kenny Shiels' side their first win of the campaign.
And, although Jon Daly pulled one back for the Tannadice side, it did little to placate Houston, who was raging on the touchline throughout the second half.
"It was three gifted goals and, although we didn't perform as we could, I don't think Kilmarnock looked like scoring until we gave them the first," the United boss said after the 3-1 defeat.
"I don't know what young Barry Douglas was thinking of. He actually took his first touch outside the box before dribbling across the six-yard box and I certainly can't blame the keeper. But he will learn from that mistake.
"We were also guilty of poor defending for the next two goals but there were a lot of aspects I wasn't happy about. We gifted Kilmarnock the points.
"After two good results in the league there were things we didn't do well and I will be sitting the players down to watch the video of the game."
After a perfect start to the season and sitting top of the Clydesdale Bank Premier League, Houston felt his side were a tad complacent.
"The players have rightly received a lot of praise for the good start and performances in the first two games, but maybe this is a reality check for them," he said.
"I'm not saying they do not try as hard but maybe they start believing what others say about them and a bit of complacency creeps into their game."
Kilmarnock boss Shiels was quietly delighted with his side's first win of the season but acknowledged United gave his team a big helping hand.
"If you take the goals out of the game I thought it was a very good performance from us," he said.
"We did well in the first half and, without intimidating them, and I thought we did enough to get in behind them in the second. The rain at half-time helped as it was going to favour a football side.
"I was surprised by United, who normally play through Jon Daly but today they played from the back."
Although he was pleased to see three of his players net their first goals for Killie, the Rugby Park boss is still on the lookout for an experienced striker before the transfer deadline.
He added: "It is great for the young players as the supporters have an affinity with them and you can hear that from the stands. But it is a lot of responsibility on young shoulders, so with Paul Heffernan out I am still looking for an experienced striker to give the young players some support."
