With the victory, Mexico advance to the knockout phase as group winners.
"I didn't like the first 20 minutes, but then we settled down, the team recovered, and that's where we showed the power of mental strength," he said at a press conference.
The Mexican coach, who led the side at the 2002 and 2010 World Cups, said that while the performance was good "we always have a few things to work on".
Aguirre, 67, said his team's mentality is essential to keep progressing at the World Cup, where they will look to move beyond the quarter-finals for the first time.
"I think we've improved in that area, that mentality of 'Well, that's it, we've done our part.' This group has character," he said.
FIFA World Cup 2026
The 2026 World Cup is taking place from June 11th to July 19th in the United States, Canada and Mexico. The tournament features 48 national teams and is played at 16 modern stadiums.
Match schedule and times | Group tables | How to watch the World Cup | World Cup Format | Past winners of the World Cup