"Obviously we will now have to rethink our entire security system," Cosomano said.
Three thieves took the paintings in three minutes at dawn on Thursday, using only a car jack to open the main door and a crowbar to smash a glass door, while four security guards changed shifts.
Police said that the thieves were likely to have been paid by an art collector wanting to add to a private collection. Experts say that the paintings will be impossible to sell.
The MASP collection is valued at more than $1bn a local newspaper reported. Their insurance premium would cost about $5m.
However, Cosomano said: "The value of the two paintings, like all the others in our collection, is incalculable and as such impossible to insure."
Julio Neves, MASP's president, said the museum could not afford a good security system.
"We don't have the resources for it. Now, we are going to update. We can improve some equipment," he said.
The museum has had financial problems in the past few years, having to close temporarily in 2005 when its power was cut off due to unpaid bills.
MASP has said that Jorge Yunes, a Sao Paulo businessman and art collector, has offered almost $60,000 as a reward for anyone who finds and returns the paintings.
A failed attempted robbery of the museum took place in October, which police are investigating for links to Thursday's heist.
Picasso's painting of singer Suzanne Bloch from 1904, one of the MASP's standout works, was a rare piece from the painter's "blue period" and therefore especially valuable - possibly worth $50m.
O Lavrador de Cafe, painted in 1939, was viewed as Portinari's best neo-realist piece and is one of Brazil's best-loved works of art. It is worth an estimated $5.5m.
His son, Joao Candido Portinari, called its loss "a real tragedy".