Four-time Tour de France champion Froome insists he did not exceed the permitted dosage of salbutamol, which he takes as an asthma sufferer.
"I've been a bike rider now for 10 years and I know how some people might look at our sport and that's a responsibility that I take really seriously".
Speaking on the Sports Personality of the Year programme on BBC One, he said he "understood people's concerns".
"So this really is quite a frightful situation if I'm honest and we're working as hard as we can to try and get down to the bottom of this".
This follows the insistence of former UCI president Pat McQuaid that Froome's adverse drugs test is "a disaster" for cycling.
"I am an asthmatic, I have been since I was a child, and I use a puffer to help manage it but I have never taken more than I am allowed, so it is quite a terrible situation".
He could be banned if he fails to explain the finding and, if so, he faces being stripped of his Vuelta title and two World Championship bronze medals, while he could also miss next year's Giro d'Italia and be unable to defend his Tour title in July.
'I was informed Froome had provided an A sample with an anomalous result for a substance that did not result in an immediate provisional suspension in the last 24 hours of my tenure at UCI, ' said Cookson in a statement.
"The fact is, he has broken a rule".
"The detailed information we have been able to provide the authorities is vast, and I hope we will be able to find out the real cause of the problem". It's up to him to go and prove that he could have done otherwise.