The 34-year-old goalkeeper struggled to take it all in after saving two spot-kicks as the Selecao triumphed in Belo Horizonte on Saturday
The game was tied at 1-1 after extra-time, following goals from David Luiz and Alexis Sanchez in the first half of the contest, before the spot-kick drama unfolded on Saturday.
Cesar produced two crucial saves, with Gonzalo Jara striking the post with his penalty, which meant Brazil advanced 3-2 on penalties.
The goalkeeper was part of the Selecao side eliminated by Netherlands in the last eight in South Africa four years ago, so was left struggling to contain his joy after helping his side into the quarter-finals.
“I thank my team-mates," Cesar told reporters after the game. "I am emotional, moved, but also happy.
"Only God and my family can understand what I’ve been through and am still going through today. They gave me so much strength.
“I was crying in desperation four years ago, but now I cry tears of joy. There are still many games left to play, but I dream of celebrating.”
Cesar also admitted that the sense of expectancy surrounding the Selecao had been a heavy burden to bear in Belo Horizonte.
“We expected a difficult game despite a good first half,” the former Inter shot-stopper explained. “After the [Chile] equaliser we ran into problems.
"It was complicated, as we are playing on home turf and the pressure is enormous."