"In football, the whole country gets the legacy," Blatter said in an interview with Rio's O Globo newspaper.
"Football involves the whole country. The country improves airports, hotels, highways, telecommunications, sustainability programs."
"I can understand that people are unhappy," Blatter added. "But football is here to unite people. Football is here to build bridges, to generate excitement, to bring hope.
"Brazil asked to host the World Cup. We didn't force it on them. It's obvious that stadiums need to be built but that isn't the only thing in a World Cup: there are highways, hotels, airports and a lot of other items that remain as a legacy."
In Brasilia, police fired tear gas at protesters who tried to reach Brazil's first game and they also fought running battles with demonstrators outside the Maracana stadium in Rio and the Mineirao arena in Belo Horizonte.
But with the stadiums the only obvious gain so far, and many of them destined to be white elephants, protesters made their anger known with placards reading: "Teachers are worth more than [Brazil striker] Neymar" and "We want schools and hospitals, not stadiums".
Blatter said he was in contact with Aldo Rebelo, Brazil's Communist Party Sports Minister, and was confident authorities have the situation under control.
"We've spoken, of course," Blatter said. "This is something for the Brazilian government and regional governments to deal with. It's up to them to resolve it.
"The only thing that FIFA can do is offer wonderful football in beautiful stadiums so people can enjoy themselves. I don't know what the government is doing. But I am confident the demonstrations won't hit the Confederations Cup."
