Brazil were on the point of going out when Fernando's shootout miss left Uruguay's Pablo Garcia needing to score to win the match. Instead, Garcia hit the post and Brazil won the shootout 5-4.
During the match itself, Brazil twice led but Uruguay fought back each time.
While Uruguay coach Oscar Tabarez and his players left without commenting, Dunga spoke of the importance of suffering.
"To be a winning team, you have to know how to suffer," said Dunga, whose own career saw him bounce back from failure at the 1990 World Cup to captain the team to victory four years later.
"In the most difficult moment, you have to have posture, courage and fight until the end.
"I want to thank the players because they left their families behind to come here and play in a very difficult competition.
"We have been together for nearly one month and their behaviour has been exemplary throughtout. They have shown great dedication, effort and love for the shirt of Brazil. All this has been after a long and tiring season in Europe."
Dunga denied his comments were an aside at Ronaldinho and Kaka, who both asked not to be picked for the competition because they said they were tired.
"There's nothing malignant in this," he said. "If they don't want to come, I can't do anything. This is a way of thanking the players who are here."
On the penalties, he said: "I wasn't certain we would win but I had great conviction that we would.
"Penalties are not just about the moment, it's a result of the preparation and work beforehand."
Mexico face Argentina in the second semi-final on Wednesday.
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