Aguirre left with bitter taste after draw
"Both sides are going away with a bitter taste and we are now forced to beat France," he told a news conference after the eyes of the world saw the tournament's opening game in the Soccer City stadium.
"We are quite confident that we can win the next two matches," the former Mexico international added. Next up is France in Polokwane on June 17 followed by Uruguay in Rustenburg five days later.
Aguirre's team had 58 per cent of possession but without a top class finisher in their starting line-up they failed to produce the knock out blows and could have lost in the dying moments when Bafana Bafana striker Katlego Mphela hit the post.
Aguirre instead paid more attention to the home side's spirit and their goalkeeper Itumeleng Khune, who produced several outstanding saves to keep the Mexicans at bay.
"The goalkeeper on the South African side was absolutely great," he said.
"South Africa were playing at home with all their fans. I think in the first half we had them in the corner but in the second half they were very very fast and it was quite fair.
"Their goal changed the match a lot," he said of Siphiwe Tshabalala's stunning strike in the 55th minute.
"I wouldn't say we got nervous but a little bit anxious. We tried to change our play and we managed to draw but it wasn't enough."
Aguirre's counterpart Carlos Alberto Parreira called Mexico "the most daring team in the World Cup" for their attacking approach, but they will have to be more ruthless when they play France and Uruguay to have any chance of progress.