Drogba said: "Everyone knows how great he is [and] how stupid the mistake was. I don't think he did it to improve his performance - it was just a mistake."
Drogba added Toure's absence from this month's game against Benin is a blow.
The two sides face each other at the end of the month in an Africa Cup of Nations qualifier.
"It will be a difficult situation for us because he is one of our most important players - one of the oldest and the most experienced," Drogba continued.
Drogba said he had spoken to Toure since the incident and that his long-time team-mate is troubled by the prospect of a potential two-year ban from football.
"He was down but that's normal," the Elephants star added.
"We feel sorry for him and he'll have all our support and that's the maximum we can do."
"He told me what happened and there's not a big difference between has been said by Arsene Wenger and what Kolo says."
Last week, Arsenal coach Wenger said that Toure, a former player of his, had failed the drugs test after taking his wife's dieting pills.
The centre-back made his international debut in 2000 and has gone to make over 80 appearances since, winning caps at both the 2006 and 2010 World Cup finals.
Source: BBC Sport
Source: BBC Sport