Dunga told Brazilian supporters he was sorry for last Sunday's incident when he swore under his breath at a journalist from Globo television during a news conference and his words were captured by the microphones.
"I want to apologise to the Brazilian fans for my attitude and my behaviour," Dunga, who escaped punishment from FIFA, told reporters.
"The people who have always supported Brazil have nothing to do with my personal problems and, as a Brazilian, I just want to work and do my best for the national team."
PAID TRIBUTE
Dunga, whose team have already qualified for the second round of the World Cup and face Portugal in their final group game on Friday, also paid a tribute to his father, who has suffered from Alzheimer's disease for several years.
"For me, this is just a chance to show my father everything he taught me," he said, appearing close to tears.
"I learned that for a man to be a man, he has to have virtue, he has to have coherence, dignity, transparency, and you have to know when to apologise for a mistake, and put things back on the right path.
"My mother, who has suffered the most because of my father's illness, taught me never to leave things half done.
"She taught me that we have to love our country, we have to be patriotic, even though some people don't like that, we have to do the best for our country, for our friends.
"We have to fight and we have to realise that adversity will just make us get better."
A former tough-tackling midfielder who captained Brazil's 1994 World Cup-winning team, Dunga was appointed three-and-a-half years ago to restore a perceived lack of discipline in the Brazil squad.
His team have since won the Copa America and Confederations Cup and have won 18 of their last 20 games. They have won both their opening World Cup games here too.
However, many Brazilians have questioned the team's defensive and physical tactics under Dunga, who has upset media organisations by greatly reducing access to players and training sessions.
