Over 15,000 people died and lakhs disabled in 1984 when gas leaked out of a Union Carbide pesticide plant in Bhopal. Dow bought Union Carbide in 2001.
Victims of the disaster, as well as former Indian Olympians and officials, have been pressuring 2012 Olympic organisers to drop Dow as a sponsor.
Coe said Dow's links with Union Carbide came 17 years after the Bhopal gas leak and it cannot be held responsible for the tragedy.
The United States-based chemical manufacturer will pay for a curtain-style wrap to encircle the Olympic Stadium in east London under a deal announced in August.
"I understand the human scale of that suffering, but these are two completely different issues. Dow were never the operators or the owners of that chemical plant in 1984, nor were they the operators or the owners of the plant in 1989 when the final settlement was agreed," Coe, who was here to attend the International Paralympic Committee general assembly, told reporters.
"Dow became the major shareholders in that company only in 2001, some 17 years after the tragedy. And the final settlement was upheld on two separate occasions by the Indian Supreme Court.
"I feel comfortable after analysing the history of this case," added Coe, the legendary middle-distance runner who won 1500m gold in 1980 and 1984 Olympics.