"After the first (Germany) goal we just had a blackout, nobody expected it," he said.
The Germans ran roughshod over the host nation, scoring five goals in a first-half humiliation, before adding two more after the break.
"Honestly, it's hard to explain," Cesar told reporters. "You can't explain the inexplicable."
Coach Luiz Felipe Scolari assumed responsibility for the historic defeat.
“The catastrophic result will be shared with the whole group, but the choice, who decided the tactical line-up, the way to play? I did," Scolari said. "So the person responsible is me.”
Brazil came into the tournament as favourites but were knocked out in the most dramatic fashion at the Mineirao stadium.
"We lost one match to a great team," Scolari said. "Not even they (the Germans), when we spoke to them after the match, they said 'even we don't know how this happened, five shots, five goals.'”
Cesar said the Brazil players would apologise but had to acknowledge that Germany were a strong team.
"It was beautiful up to here. I thank the Brazilian people and the fans are to be congratulated for all the support they gave us," he said.
"We will go home, hug our families. And thank the fans. We got close but we couldn't that's it."
Defender David Luiz sobbed openly as the pain of the humiliation sank in.
"I just wanted to make my people happy," he said. "Unfortunately we couldn't. I'm sorry, I'm sorry to all Brazilians, I just wanted to see them smile."
Captain for the day, Luiz apologised to fans but recognised the Germans total superiority.
"They were the best, they prepared better, they played better, we let in four goals in six minutes. It is a very sad day and we'll learn from it."
(Writing by Andrew Downie, editing by Ed Osmond and Nigel Hunt)
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