Mexico's 2-0 win over Ecuador at the Azteca Stadium was their fourth straight victory without a goal conceded at the tournament.
"This connection we have with the fans is a driving force," Aguirre said at a press conference.
On Tuesday night, the Azteca was once again overflowing, with just over 80,000 fans cheering on their team from start to finish and booing every time the opposing team touched the ball.
"I've had some great victories, but none like today's, because it's at home, with your own people," added Aguirre, who previously managed Mexico at the 2002 and 2010 World Cups.
On Sunday, Mexico will play in the round of 16 again at home in Mexico City against the winner of the match between England and D.R. Congo.
Aguirre, 67, praised the Ecuadorean team, who finished second in the South American qualifiers with only two losses in 18 matches.
"It is not easy to beat Ecuador," he said.
Aguirre was happy with Mexico's performance, his only gripe being that they were unable to score more goals on the counterattack to kill off the game.