It emerged yesterday that Gay had tested positive from an A Sample relating to an out-of-competition test in May, while Powell was found to have banned stimulant in his system while at the Jamaican Championships last month.
"These are all big names," BBC Sport quotes Jackson as saying. "To take Asafa Powell and Tyson Gay out leaves a big void in our sport.
"We have to sift out the negative people and we will never be in a win-win situation. When you expose these people, it can have an adverse effect but it is important to do so, for the future of the sport and the next generation."
Both are believed to be awaiting the outcome of their respective B Samples.