Marquez told reporters at his official presentation that he hoped to achieve from the bench what he could not as a player.
"It did not happen for me as a player in those five World Cups; unfortunately, we always reached the same point," Marquez said. "Today, I have this opportunity."
The former defender represented his country at the 2002, 2006, 2010, 2014 and 2018 World Cups. Mexico were eliminated in the round of 16 at each of those tournaments.
Marquez, who enjoyed a distinguished club career with AS Monaco and Barcelona, winning four LaLiga titles and two Champions League crowns at the Spanish club, said his immediate task was to build on the foundations laid by former coach Javier Aguirre rather than start from scratch.
"The way I finished working with Javier gives me a great deal of confidence to continue this process. I know the players quite well, I know the environment," he said.
Marquez served on Aguirre's coaching staff at the most recent World Cup, which was co-hosted by Mexico and was the first to feature 48 teams.
The country ended a 40-year wait for a World Cup knockout victory by beating Ecuador 2-0 in the last 32 at the Azteca Stadium in June, reaching the round of 16, and Marquez said that his familiarity with the squad and the national-team environment would be key to advancing further.
He added his priority would be to establish a competitive identity and a closer connection with supporters.
"We want people to feel proud of their national team, to be happy to see a team that gives everything and represents them well," Marquez said. "We want to compete at all times, regardless of the opponent."
Marquez will take charge for the first time against Colombia in Baltimore on September 26, before Mexico continue their four-match tour against Peru in New Jersey three days later.
They will also face the United States in Glendale, Arizona, on October 3, before facing Chile in Los Angeles three days later.