The RFEF contacted both Milla, who led Spain to the European under-21 championship title one year ago, and physio Juan Carlos Martinez on Tuesday to say neither would be offered a contract extension, it said on its website (www.rfef.es).
"The RFEF would like to publicly thank them both for their work since they were hired in 2008 and 2009 respectively," said the statement.
Spain, one of the Olympic tournament favourites, lost their opening two Group D games 1-0 to Japan and Honduras, dashing their medal hopes, before being held to a goalless draw by Morocco.
Under-19 coach Julen Lopetegui will take charge of the side for next month's European Championship under-21 qualifiers against Switzerland and Croatia, the RFEF said.
The Olympic Games features under-23 teams with each allowed to field up to three over-age players.