The former Barcelona coach replaced Juan Carlos Osorio, who resigned following the World Cup in 2018 and went on to quit the Paraguay job after a matter of months in the post.
Expectations are high given Martino's experience and the talent at his disposal and, after a quiet first half on Friday, Mexico clicked into gear in the second period – a Raul Jimenez penalty followed by goals from Hector Moreno and Hirving Lozano, while Nicolas Castillo pulled one back for Chile.
Although it was a commendable victory, Martino wants fans and players to not get ahead of themselves.
"I don't believe that people are going crazy over one positive result in a friendly," Martino told reporters. "We aspire to have a successful cycle and this team excites me, the future excites me.
"[But] we'd be here until tomorrow if I explained all the things we have to improve.
"We've won and it's also important to highlight the positive things, but we have to put this into the perspective that this was a friendly."
Mexico play Martino's former team Paraguay in their next friendly on Tuesday.