Coe, who is on the board of England's World Cup bid team, told Reuters on Wednesday he had talked to FIFA president Sepp Blatter after Triesman's secretly taped conversation with a former colleague in which he spoke of a conspiracy between rival bidders Spain and Russia to bribe referees.
"I had a chat with Sepp Blatter and it was a very friendly and lengthy conversation," Coe said as he prepared to launch the London 2012 mascots.
"We know each other very well and it was very open chat. His clear inference was 'go on telling our story, talk about the qualities of the bid, the eminence of the venues and why we are doing it'.
"The impression I get from him is that we will be judged on those things."
England's bid leaders have taken damage limitation measures since Triesman's comments and Coe, a skilled sports administrator and formerly part of FIFA's ethics committee, has assumed a more high-profile role.
FIFA has ordered an investigation into Triesman's comments and there have been fears in England that the bid could have been badly damaged.
"We needed to resolve the situation as quickly as we could and go on driving the bid forward," Coe said. "We haven't become a bad bid over one news cycle. The fundamentals are solidly in place and nobody is doubting that.
"There is rarely anything that is so serious that you are permanently derailed or so great that you jump across the line in one fell swoop.
"It's all hands to the pump now and what we do in the last six months."
England faces competitiion from the joint Spain/Portugal bid, Russia and Belgium/Netherlands, Australia and the United States. The vote takes place in December.
