Cuauhtemoc Blanco scored the only goal of the game from the penalty spot after 60 minutes.
The spot kick was awarded after a rash challenge by Boris Zivkovic, for which the Croatian became the first player of the tournament to receive a red card.
We have a win in the first match but that is not enough to make me satisfied
It was no less than Mexico deserved after an industrious performance against a lacklustre Croatia.
But Aguirre is hoping for an improvement from his players.
"We have a win in the first match but that is not enough to make me satisfied," said Aguirre
"Now we must win the next matches - that is why we are here."
"There were a lot of errors by my players in the final third of the pitch and that is where we have to play better."
Aguirre recognised that his team had triumphed in a tricky opening fixture against the team who finished third at the 1998 World Cup.
And he was especially pleased with the performance of goalkeeper Oscar Perez.
"Croatia played really hard football and this was a difficult game for us," said Aguirre.
"Goalkeeper Oscar Perez made a couple of really good saves and when they were reduced to 10 men it made a difference."