But despite leading Unitedto their third victory in a week, Houston again insisted he does not want the job on a permanent basis.
He said: "We will let him (the chairman) take his time and see what happens. I'm quite happy to take it game by game.
"I did make a stance and I'm not going to change it just because we have won three games in a row.
"I'm well in with the boys here so if I want to be a manger it will have to be at some other club.
"I just want the club to make sure they get the right man. I know these things can take time but that can be OK as long as you keep winning."
Houston was delighted with how his side battled against a below-par Hibernian to record their third successive victory and reserved special praise for Dusan Pernis who once again kept a clean sheet.
"It has been a great seven days and it is not often that you get three clean sheets in a week," he said. "I'm absolutely delighted and I thought the players were magnificent.
"I thought we took the games to Hibs in the first half and created a few chances.
"We knew Hibs were going to come back at us as they are an excellent team but I thought we coped admirably.
"We have brought in an excellent goalkeeper in Dusan Pernis and that, allied with ten other players working their socks off, was what made the difference."
However Houston admitted his side may have benefited from a couple of refereeing decisions.
He added: "I believe it may not have been a penalty but I haven't seen the video yet so I can't really comment.
"Somebody said David Goodwillie may have also been offside before he set up Danny Swanson but I will have to watch that one on the video again as well."
Hibernian boss John Hughes refused to be too despondent after the defeat.
He said: "I thought we gave it a really good effort. Did we create enough chances to equalise? Possibly, when you think of Colin Nish's header that just went wide and David Wotherspoon's volley.
"But you have to give credit where it is due and Dundee United dominated the first half and probably deserved to be in front.
"I have seen my boys play better but in terms of effort and commitment the second half was fantastic."
Hughes added: "It was not a penalty. I'm lucky enough to have seen it. It was a good yard outside the box so it is disappointing that Steve (Conroy) has got that wrong.
"I thought their goal was also a yard offside but it is the linesman who has to raise his flag."