Jozic saw his side lose to Cuauhtemoc Blanco's 60th minute penalty, and also suffer the tournament's first red card when Boris Zivkovic was sent off for the offence.
It's always bad to lose in the first game but the players
have to get over the shock
Croatia coach Mirko Jozic
Croatia face fancied Italy next, followed by Ecuador, and their chances of qualifying from Group G received a knock by the defeat to Mexico.
But Jozic remained upbeat, saying: "The first battle is over, but the war is not lost.
"It's always bad to lose in the first game but the players have to get over the shock.
Jozic attributed the loss to problems in the midfield and paid tribute to Mexico goalkeeper Oscar Perez, who pulled off three good saves.
"We never underestimated Mexico but our distribution and control of the ball was bad.
"The midfield was quite disorganised and the Mexican goalkeeper was excellent," he added.