Swanson came on as a substitute but was sent off for two bookable offences as United let a two-goal lead slip in their first game since November 20 following snow and ice across Scotland.
"We had over five weeks' lay-off and a lot of people expected us to be rusty," said Houston. "But I felt in the first half we totally dominated the game and the game could've been won. Giving that goal away was costly for us, but even more so was going down to 10 men. I'm frustrated and disappointed. I think it was two points dropped."
David Goodwillie took his tally to 10 for the season with goals after two and 35 minutes, but Sol Bamba pulled one back before the break. And after Swanson's dismissal, Paul Hanlon diverted a Danny Galbraith drive into the net as Hibs claimed a point, much to Houston's annoyance.
The United boss added: "I've no complaints with the sending-off at all - I'm disappointed and frustrated with Danny. He naturally feels he's let the boys down and I feel he's let them down as well."
Hibs boss Colin Calderwood now has two wins and two draws from 10 games in charge ahead of the New Year's Day derby with in-form Hearts.
He said: "We've gained a point from a very tricky situation, let's make no mistake about it. The situation after 30-odd minutes, whenever the second goal went in, is a horrible experience but a character-building one for everybody.
"We're conceding too many soft goals again, so you don't need the pro-licence to see what we're doing wrong."
Merouane Zemmama made his first appearance since March following a cruciate knee ligament injury and Calderwood praised the Moroccan's impact.
He said: "He needs some football. He hasn't even had a full week's training with the group, but the lift that it gave to the team at half-time and his touches and his influence on our play was apparent."
Source: PA