Luka Modric (Getty Images)
Zlatko Dalic's men outclassed their opponents in Nizhny Novgorod, leaving Lionel Messi and two-time world champions Argentina on the brink of an embarrassing group-stage exit.
"Let's not be euphoric or get ahead of ourselves," said Real Madrid midfielder Modric, who scored the second goal.
"Of course this win will boost our confidence for the next game, and we have shown we can create opportunities, but let's keep our feet firmly on the ground.
"Our team effort throughout (was the key) and particularly in the second half when we had more possession.
"In the first half when Argentina had the ball we cut off Messi and stopped him getting the ball. We created three clear chances which we missed. But in the second half it opened up and we deserved to win."