The Central Americans face the Netherlands on Sunday in their last 16 clash, with the winners in Fortaleza going through to play either Greece or Costa Rica.
A place in the last eight would represent Mexico's best performance at a World Cup since hosting the showpiece in 1986.
However, Herrera will not be satisfied with a place in the quarter-finals, declaring that the current team has enough ability to go all the way after coming through the tricky Group A.
"The least we want is to win our next game and play a fifth match," Herrera told El Universal. "It is the least one would expect.
"But we will not like Brazil (the tournament) if we know we played only five games, because I'm sure that the capabilities and desire of this group is at seven (matches, the final).
"I'm sure this weekend we will make a different story for Mexico outside of our country.
"Then comes the idea of history and the prosperity of the names of these guys (his players). I'm sure they will do a lot because I see well that they are in tune with what we want.
"Of course I'll be happy (to beat the Netherlands), because we spend one more round here and have another game and another opportunity to continue making history, but I will not be satisfied.
"The minimum requirement, not the main requirement, was to reach the fifth game.
"(But) it seems the more we talk about the fifth game, after (we reach it) history will already be made so we'll just go home.
"No, we do not just come for the fifth game."
