United have climbed to fourth place in the Clydesdale Bank Premier League table thanks to a 3-0 win over Inverness at Tannadice, but Houston expects a completely different test when Neil Lennon's cup holders visit Dundee.
He said: "It was a good boost getting a win before Sunday but we will need to play a lot better against Celtic to knock them out.
"They are a quality side. Our coach Paul Hegarty watched Celtic against Aberdeen on Saturday [1-1 draw at Pittodrie] and, even though they never played to their usual standard, it will be a big test for us.
"Celtic are a really good team this season. They will be fired up for the cup tie and they will be strong regardless of who plays.
"They have a lot of depth in their squad and I'm not sure who will play but we will have the boys ready. We need to go into the match and be on our game from the start. We will attack because that's the only way you win cup ties."