"I don't really believe 90 percent of the peloton are still doping for instance as a witness says but I do believe there's still an endemic problem of lower level doping," said Cookson, president of the sport's ruling body the UCI, based in Aigle, Switzerland.
"I believe efforts have been made to tackle those problems, there have been major step forwards like the biological passport," he added.
"It's now possible to compete in professional cycling without doping," Cookson said.
"Nevertheless there's still a problem there, clearly in any sport there are people trying to cheat and we need to stop them and to protect riders who want to compete without cheating, we have a lot more to do and we will continue."
Cookson was speaking after an independent commission accused former UCI presidents Hein Verbruggen and Pat McQuaid of shielding disgraced Armstrong from investigation.
Armstrong, who defeated cancer to go on and win seven straight Tour de France races from 1999 to 2005, was stripped of his titles in 2012 and banned from the sport for life.
The fallen US cycling hero, 43, now admits taking banned substances.
"The UCI management has changed, we no longer close our eyes to doping," Cookson said.
"The style of leadership of Hein Verbruggen is criticized in the report and that style of leadership led to some of the major errors," he said.
"Image and the business of the sport were put before integrity and transparency and honesty, that approach was taken too far," Cookson said.
"I hope these two won't have any role in cycling in the future."