Mexico scraped through the CONCACAF qualifiers after finishing fourth behind United States, Costa Rica and Honduras in the second group stage.
A 9-3 aggregate win over New Zealand in the intercontinental play-off secured a place in Brazil, but few expected Miguel Herrera's men to make an impact in a tricky Group A.
However, after beating Cameroon 1-0 and drawing 0-0 with the tournament hosts, Mexico need only a point when they face Croatia on Monday to progress to the last 16.
"Our current coach has been very influential," Marquez said.
"We've worked really hard to achieve what he's asked of us, and he's brought together a very good squad of players for this World Cup.
"What's more, I think that we've learned from our mistakes and we're now stronger than we were during qualifying.
"We're really happy (with our tournament so far). If you take a look at the quality of the teams we've faced, it shows how difficult and tough a task we've had. And though we're not there yet, we're close to taking an important step."
Mexico kept cleansheets in their opening two games and centre-back Francisco Javier Rodriguez believes the side's defence are answering their critics.
"This is an important achievement," he added. "(It's) another objective which also we have met, so we hope that it will continue.
"We are very calm and working (well). The defence will always be the most criticised, but we are just focused on what we have to perform and improving every day, which we are doing."
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