Suarez netted upon his Uruguay return, following a lengthy FIFA ban, as Brazil surrendered a 2-0 lead to draw 2-2 in their 2018 World Cup qualifier Recife.
Bayern Munich attacker Douglas Costa opened the scoring for the hosts in the first minute before Renato Augusto made it 2-0 after 26 minutes.
However, Cavani pulled one back just past the half-hour mark as the Paris Saint-Germain striker made no mistake to convert from close range.
Suarez completed the come-back four minutes into the second half, extending his all-time goalscoring record for La Celeste, after tucking home a through-ball from Alvaro Pereira.
Dunga lamented a game of two halves as he admitted his side lost control of the game in the second half, while adding that it was always going to be tough against Suarez and Cavani.
"That first half the team got off to a good start, rolling the ball and making most of the space," the 52-year-old said.
"In the second half we were more static, without the same movement. Uruguay took advantage of it. In one half Brazil played, in the other it was Uruguay.
"To play against an attacker like Cavani, like Suarez is not easy. It's never easy to play against Uruguay."
Dunga also rued a yellow card handed to striker Neymar, which will see the Barcelona star suspended for their next qualifier against Paraguay.
"As for the foul he [Neymar] gave away to get the yellow card, there should have been yellows for the fouls he received," he added.
"The foul was not bad enough to receive a yellow. But it's Neymar, and the referees will always be rigid with him."