The 57-year-old's departure from Craven Cottage was made official on Tuesday night, with head coach Rene Meulensteen and technical director Alan Curbishley also making way for new manager Felix Magath and his backroom staff.
Wilkins, who was last year banned from driving for three years after being convicted of drink-driving, remained in the dressing room after half-time in last week's home defeat to Liverpool and admitted he can sometimes look "worse for wear" in the dug-out.
The former England and Chelsea midfielder insists the chronic bowel condition is to blame.
Wilkins told the Daily Mail: "I need to control the ulcerative colitis with strict medication, which I had not done before the Liverpool game
That is the reason I didn't return to the dug-out after half-time, as I needed to be close to a toilet.
"Unfortunately I can look the worse for wear but it is nothing to do with drink
I did have verbals with (Liverpool manager) Brendan Rodgers, but it was nothing.
"I was face to face with (Fulham) chief executive Alistair Mackintosh and the owner Mr (Shahid) Khan straight before the game
And if I had been unable to carry out my duties, they had the right to sack me on the spot.
"I most certainly had not been drinking on the train before the match."
Wilkins said he "didn't want to make a fuss" about his condition.
"But I desperately want to carry on in football and there's no chance of that happening if everyone gets the wrong impression that I have a drink problem," he added.
"I was very stupid about the drink-driving and I have had trouble with depression on occasions - but not since I was back in football."
Source : PA
Source: PA