Despite being in a position to see out the game, Brazil were left four against four at the back and once Petkovic had taken advantage to make it 1-1, Croatia capitalised on their chance in the penalty shoot-out to book their place in the semifinals.
"I don't agree we were disorganised," said Tite when asked about Croatia's late equaliser.
"We were defensive, we had players that put high pressure at the front. We tried to retain the game and we managed to close the centre of the pitch but I understand the pain and all criticisms people have towards my choices."
Brazil were one of the pre-tournament favourites in Qatar but have now been dumped out in the quarterfinals four times since lifting the trophy in 2002.
They also again failed to beat a European nation in the knockouts after last doing so against Germany in the 2002 final.
"I think we need to be ready to share our joy and also willing to share our sadness and I think there is a new generation of players that will find strength in adversity and I understand I am the most responsible one," added Tite.
"It is not about being a villain or a hero, there is no such thing in sport. That is football, sometimes we win, sometimes we lose.
Tite confirmed afterwards he will leave his post following the World Cup exit. The 61-year-old took over in 2016 but announced before the tournament he would depart once Brazil's run in Qatar was over.
"It's a painful defeat but I'm at peace with myself, it's the end of the cycle," he said.
"It was a whole four-year process. Before it was a recovery process but now there's been a whole sequence. I cannot make an assessment of the entire cycle but over time you and other people will do that."