Coe was speaking in Moscow, the host of next month's world athletics championships, after American Tyson Gay, a former world 100 metres champion, and Jamaica's Asafa Powell, a former 100 metres world record holder, provided positive samples.
The two athletes have withdrawn from the Moscow championships.
"The right thing (to do) is being aggressive about our testing, is forever making sure our technology runs ahead of the competitors and our overall task is to make sure the sport is clean for clean athletes," Coe told Reuters.
"I think it would be unrealistic of me to say that we are ever going to reach a period where we will be entirely free from the scourge of drugs in sports," the former Olympic 1,500 metres champion added.
"But...we are taking this more seriously than we have ever taken it before."
The world championships will be the first major outdoor athletics event hosted by Moscow since the 1980 Olympics and it will be held at the same Luzhniki stadium which staged the opening ceremony of the summer Games more than three decades ago.