Fury brought Klitschko's nine-year reign as heavyweight king to an end on Saturday in one of the biggest upsets in boxing history.
The 27-year-old slugger decided to avoid drinking water and remain dehydrated post-fight after receiving good information he might be drugged.
"After the fight, I had it from good sources not to touch anything in the changing room because they might try to drug me," Fury said.
"People were trying to pass me all sorts of things but unless it came from my own baggage, I wasn't having it, there was no chance of me getting drugged.
"I went home dehydrated before I even touched anything because I was so frightened of being tested and failing the test because they've given me something. You can never be too careful."
A rematch between Fury and Klitschko is a strong possibility in the near future - with the British boxer planning on taking some time off before deciding his next move.