Thursday night's game between the Copa America champions and the five-times World Cup winners was fairly even until Eduardo Vargas opened the scoring for the home side in the 72nd minute.
Chile then took control and Arsenal's Alexis Sanchez doubled their lead in the dying moments.
It was Chile's first win over Brazil in the World Cup qualifiers since 2000.
Brazil were without the suspended Neymar and Dunga admitted his side lacked pace and erred too often with their final pass, both areas in which the Barcelona striker excels.
"Willian took responsibility, Oscar took responsibility, Douglas did too," the coach told reporters.
"People always analyse the result. Of course he (Neymar) is important. We had four or five counter attacks that could have proven fatal. If the ball had gone in we wouldn't be discussing this."
Dunga, however, said he would not totally reshuffle his side ahead of Tuesday's encounter with Venezuela in Fortaleza.
"You don't always have to change everything around after a negative result,” Dunga was quoted as saying by Brazilian media.
"The first half was very even. Until Chile's first goal we had some good chances. That's football. You don't need to change after every defeat but rather improve with every game."
Fullback Dani Alves agreed that major changes were unnecessary.
"If you chop and change according to results it is hard to find a balance," he said. "This group has to keep going. I think victories are inevitable."
The South American qualifiers are in a round-robin format with all 10 teams playing each other home and away. The top four qualify automatically and the fifth-place team goes into a playoff.
Brazil's defeat and Argentina's surprising 2-0 loss at home to Ecuador suggest the qualifying competition could be more open than at any time previously.
Brazil have never failed to qualify for the World Cup finals but they are taking nothing for granted this time after their 7-1 humiliation at the hands of Germany in the tournament's semi-final last year.
After facing Venezuela on Tuesday, Brazil go to Argentina on Nov. 13 before taking on Peru at home four days later.
(Writing by Andrew Downie; editing by Toby Davis)
