"What happened to Boston is a drama, it is a tragedy and an attack on sport, in one of the most popular sports, the marathon," Blatter said during a visit to Cuba.
"It is incredible, but it is our society, a society that is violent," he added in Havana during a week-long tour of the Caribbean and Central America.
"We must be careful, but sports organisations, the best and biggest, don't have the right to intervene with police, with armed forces. That doesn't happen.
"So we should take all possible precautions to secure an event."
Blatter was questioned about security during next year's World Cup finals in Brazil.
"Security (at sports events) is the responsibility of the government that organises the competitions," he said.
"We in FIFA should take care to provide all the necessary information.
"The police, armed forces, secret services of the 31 teams that qualify (for Brazil 2014), that will be a work force that will be in Interpol's hands. We can't do anything more."
Blatter, who visited the Dominican Republic and Haiti before moving on to Cuba, recalled the 2010 FIFA World Cup in South Africa, praising it for its security and called it a "party to humanity."
His trip ends in Panama on Friday where he will attend the CONCACAF Congress and its U17 championship final in Panama City.
- Sports & Recreation