"Football clubs in Scotland just now are finding it very tough; Dundee United are exactly the same."
On becoming caretaker in December, Houston initially indicated he did not want the job after his side suffered a 7-1 hammering by Rangers in his second game in charge.
And United looked set to appoint Pat Fenlon as Levein's successor until negotiations broke down with Bohemians about compensation.
However, after Houston carried on in his interim role, United went on to finish nine points ahead of fourth-placed Hibernian in the SPL and ended the season by defeating Ross County 3-0 in the Scottish Cup final at Hampden.
"To beat last season is going to take some doing," Houston added.
"If you win the Scottish Cup and finish third - well clear of the team in fourth - it's going to be really difficult.
"I'm sure if the United fans see the same effort and commitment from the players, and a wee bit of a rub of the green, then I know they'll be right behind us."
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