"I am very happy with the result but now we have no option but to go all out for victory and three points against Italy in our final group game," he said.
Mexico went behind early on against Ecuador, thanks to an Agustin Delgado strike.
But they recovered their composure with goals from Jared Borgetti and Gerardo Torrado.
The manager admitted that his side had to work hard to secure their victory.
"We had to sweat a lot," he said. "It was a serious match and was an uphill battle although the end result was what I had hoped for.
Aguirre, whose side beat Italy's conquerers Croatia in their opening game, also paid tribute to Ecuador.
"Some of Ecuador's substitutions made us change our game," he said.
"When Carlos Tenorio was thrown into the fray, he is very fast so he upped the tempo.
"Alex Aguinaga was another who made us work very hard for the win."
Mexico need a point in their final group game against Italy to guarantee their place in the second round.
But Aguirre insists his team will not play for the draw.
"Of course we already have two victories but we have to search for the victory again by attacking and going after the ball," he said.
"The players that Giovanni Trapattoni has at his disposal, like Christian Vieri and Francesco Totti, will make it very dangerous for us."