I think the truth is somewhere in the middle.
Brazil had more possession, and controlled the game for the most part. While in control, it ceded wide open spaces for the croatians, and that's how that first (own) goal came about. Defense was never Brazil's strong point.
Individually, Brazil was horrible, with several important players completely absent from play, like Paulinho. Croatia had a more "together" team, but after they scored, they went 11-behind-the-line and played defense. Against a strong(er) team, that's always risky, and they paid for that.
If they kept on going after their first goal, exploring Brazil's glaring weakness in the defense, they would've won for sure, as the brazilians were lost, and with key players neutralized. But no, they went all-out defensive, and in the 2nd half, Brazil came back stronger.
Oh, the refereering... A japanese? C'mon... Put an italian, a brit, a german, someone with experience in tough, important matches. That same ref. always had a bad call against Brazil at the last cup, so he was known to fumble like that... When the ref. is bad, the pendulum swings both ways, he could've just as well made a bad call against Brazil again...
alexandre