United secured their third Clydesdale Bank Premier League win in nine days on Thursday night 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, bearing in mind they face Motherwell in the cup quarter-final on Sunday.
"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."
Houston has used his squad to good effect in recent games, resting Craig Conway, Prince Buaben and Danny Swanson from the start against Accies.
Daly returned earlier than expected following hernia surgery and he will be joined in the squad at the weekend by Garry Kenneth, who has shrugged off a knee injury.
And Houston is confident United will produce a better performance at Tannadice on Sunday after a slow start against SPL bottom club Accies, who took the lead before David Goodwillie levelled three minutes before the break.
"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," the United boss added. "We've got a bunch of players who are very fit. They train to a high tempo normally, we have toned it down a wee bit.
"One thing that's for sure, I'm sure you will see a different Dundee United side from the first half onwards because it's a cup tie against an SPL club, a good side in Motherwell, and we'll be at it on Sunday."
Source: PA
Source: PA