Smith confessed to fears that Treble talk had led to his players taking their foot off the gas.
And he issued a stark warning they can't afford to ease off as they chase a domestic clean sweep.
He said: "When you see today's game you see the difficulties you have to overcome if you are going to win a Treble.
"I just feel all the talk of Trebles and winning the league just because we have a gap is really premature. I know people will say, from a managerial point of view, that I'm just playing it safe. But today showed you that is not the case. I'm being realistic.
"If we are going to succeed we now face a really tough cup tie at Tannadice and we still have to go there in the championship.
"People are making assumptions, but they are not taking into account how hard it is going to be for us between now and the end of the season."