The tournament newcomers lost to Switzerland in their opener but stunned co-hosts New Zealand 1-0 for their first win of the tournament in their second match.
Their campaign ended on a disappointing note as they fell 6-0 to 1995 champions Norway on Sunday, as they missed the knockout stages.
"Beating New Zealand on home soil and scoring our first World Cup goal and getting our first win was the things that dreams are made of," Stajcic said in a statement.
"Despite the scoreline, the last match against Norway, where 34,000 patrons attended, with 30,000 singing for the Filipinas, brought shivers down our spine. It showed that football does belong in the Philippines," he added.
Assistant coach Nahuel Arrarte, whose contract also expired at the end of the Philippines World Cup run, will also not be returning, the federation said.
