United secured their third Premier League win in nine days when Jon Daly's injury-time goal secured a 2-1 victory over Hamilton.
The club issued a statement expressing their disappointment when the date was set for the twice-postponed game, which comes less than three days before their cup quarter-final against Motherwell.
"There is nothing we could do because we've got to fit the fixtures in at some stage," Houston said. "The SPL had to get it in somewhere. I would have liked it in another week but we've got Motherwell in the cup and there is no point mumping and moaning about it.
"We've got a couple of days' recovery time. We will do very, very little. I will shape the team up on Saturday and probably pick the team on Saturday after a recovery session. We will do very little on Saturday as well.
"We are focused and, if we don't win the cup tie, I won't stand here saying it was because we were too tired and blaming anybody."
Source: PA
Source: PA