Following the disappointment of crashing out of the Europa League to AEK Athens and enduring the chaos created by the venue of the game changing twice, United roared back from going a goal behind on Sunday to earn a deserved 1-1 draw.
And Houston believes his side just ran out of time in their bid to rack up their first Scottish Premier League win of the season after finishing the stronger of the two teams at Tynecastle.
David Templeton gave the hosts a 30th-minute lead and, after United striker Jon Daly had a penalty saved by Marian Kello, Morgaro Gomis scored a wonder strike four minutes from time.
The Tannadice outfit had chances to emerge with a victory but were kept out by good goalkeeping and some last-ditch defending.
Houston, who revealed Middlesbrough had not been back in touch regarding an improved bid for Craig Conway, said: "I thought the players showed great character and I'm really proud of them.
"I thought they were magnificent, we had a tough time with the travelling back from Greece.
"I felt at the end of the second half there was only one team hanging on.
"If we had come out with nothing to show from the game I would have been really disappointed for the players. If we had more time I think we could have gone on to win it.
"I can't praise the players enough, especially 48 hours after coming back from the European game."
Gomis came off the bench to notch the equaliser and Houston was delighted with the player's attitude after leaving him out of the starting line-up.
He added: "Morgaro was left out because his form has not been great but he answered me in the right manner, he has cracked one in."
Hearts manager Jim Jefferies admits defender Lee Wallace is a doubt for Scotland's forthcoming Euro 2012 qualifying double header against Lithuanian and Liechtenstein after missing the match due to an ankle problem.
Wallace was initially included in the team but pulled up in the warm-up after a pain-killing injection failed to have the desired effect.
Jefferies added: "He has got deep-rooted inflammation in his ankle, he aggravated it in midweek against Elgin City.
"We thought it would clear up. We tried an injection, we put him in the team and hoped it would numb in the warm-up.
"But he came back in saying it was not having any effect. He will report to Scotland and we'll see how it goes."