The Seleção became the first South American team to make it to the global showpiece next summer after a crucial win at the Estadio Gigante de Arroyito. A brace by Luis Fabiano followed Luisao's opener gave Brazil victory, while Jesus Datolo reduced the deficit for the hosts in Rosario.
Dunga, who captained Brazil to the 1994 FIFA World Cup title, said: "We knew it was going to be tough, but I told my players that if we finished the game with all the players on the field, we were going to win it.
"We tried to play tough, firm, but trying to not get carded. We always tried to play. Brazil were very focused on the game all the time, trying to play with speed in the right moments. We were surprised by Argentina pressuring us in the opening minutes," he said. "The field was great, it helped us gain speed in our play."
Dunga added the victory was very important as they were the first to beat Argentina as visitors in the current FIFA World Cup qualification. "They are a big national team, with [Lionel] Messi possibly named the best player all over the world," he said.
"Argentina had not lost at home in this qualifying tournament before. It was tough, but technical quality prevailed. We went towards the goal in any moment."
Argentina coach Diego Maradona, however, disagreed with Dunga as he believed Brazil profited from their few goalscoring chances. Maradona said: "Brazil approached us and scored. Their first attempt turned into goal. The second was a goal too. The third attempt was saved by [Argentina goalkeeper Mariano] Andujar.
"Brazil did not hurt us for more than 20 minutes. Their first chance was scored. We failed to stop aerial balls. Losing by two goals, we needed to take risks," Maradona said. "If we hadn't, it would have been useless."
Argentina have a crucial game against Paraguay on Wednesday and Maradona is certainly aware of its importance. He added: "We must keep working hard and go to Paraguay to try to win. It will not be easy, especially after tonight's defeat because we thought we were going to win. Losing to Brazil is not nice at all."
Fabiano acknowledged that his second goal, which came just two minutes after Jesus Datolo had halved the deficit after 66 minutes, was crucial. He said: "It was very, very important because Argentina started to pressure after their goal. We have to celebrate this win a lot."
Finally, Kaka added: "I am very happy for having an active participation in the goals we scored. I helped the national team win. Today is a wonderful day for this group who booked the World Cup berth here in Argentina. It was a brilliant match and the team played with intelligence."