Miguel Herrera's men put on an impressive display in Natal on Friday as they beat Cameroon 1-0, moving level on three points with hosts and tournament favourites Brazil in Group A.
The Mexicans unluckily had two Giovani dos Santos goals disallowed for offside in the first half, but Herrera's men rarely looked troubled by their African counterparts.
Peralta, who will join Club America after the tournament, netted the match's only goal in the 61st minute and although that strike sparked celebrations among the Mexicans, he has reminded his team-mates that they have achieved nothing yet.
"We are still far from our goal," he began. "We're very, very happy, but we have two more remaining games.
"We will celebrate when we have in fact won something and when we have actually achieved something.
"We sought to give our maximum and we gave our maximum. It was a time consuming job, but the reward came. This is for all who have believed in us.
"We played well because we trained well. We played a good game and could have scored more goals, but anyway, we must not look back.
"This is for the people of Laguna (the area Peralta is from). It is a goal for all of us. It only serves to help get a win which puts us closer to our goal."
The match also saw Rafael Marquez become the first player in history to captain a team at four World Cups and the former Barcelona man said Mexico should still savour a first-up win.
"You have to enjoy it, we are entitled to that," the 35-year-old said. "But nothing more. We have to make the most of the experience.
"The win was very narrow, but the team was pretty good and we won, which is what matters.
"We had to adapt to the conditions of the pitch and the rain. We showed character and held on (to the win)."
