The revelations came two days after the FA submitted its 1,752-page bid book to football's governing body Fifa.
But Warner believes that Triesman's swift resignation may have helped England's bid to recover momentum.
"The FA did it correctly, getting him to resign immediately, and there was not much damage done," Warner told BBC Sports Editor David Bond. "Very few people on the Fifa executive committee are talking about it.
"England's chances are as good as the other countries. England has the capacity and the capability to host a successful World Cup but I guess so do the other countries."
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