The South Americans suffered a late defeat to the Netherlands on Sunday in the last 16 of the tournament.
Despite Mexico's departure from Brazil, Herrera believes that he is the right man to lead the country forward.
"My intention is to stay in charge of the team," he told FIFA.com. "I've spoken to the people at the Mexican FA and I think they're pleased with the job I'm doing.
"I'd love to be able to stay on and finish what we've started."
Herrera was appointed Mexico manager in October 2013.