A 1-0 victory over Inverness Caledonian Thistle ensured United will be in the top half of the table when the Clydesdale Bank Premier League splits for the final five rounds of games.
Houston said: "I thought we were running on fumes towards the end but I can't fault them. We went into the month of March with all these games in hand and the biggest thing for me was getting through it with as many points as we could.
"Never in my wildest dreams did I think we would get the lot. It is all credit to the players as they have done magnificent.
"I don't think we will get third as Hearts got a late winner. They have had a magnificent season but I can't ask for any more from my players.
"Fifteen points out of 15 for the first time in 14 years is a magnificent achievement."
Source: PA
Source: PA