Pato has been out injured since March and consequently did not earn a spot in Carlos Dunga's 30-man preliminary Brazil squad.
He said: "I believed in my chances right to the end. It's a shame, but I am still young and will work even harder to make sure I am ready for the 2014 World Cup, especially as the hosts are Brazil."
There have been reports Pato is on his way out of San Siro this summer, as interest from Chelsea remains high.
"I want to assure the fans that I will always do everything I can to help Milan win something.
"It has not been a good year for me. I was on the sidelines for two months, but I'm happy that I returned to the field against Genoa at the weekend and did not feel pain."