The human rights organisation said that the takedown led to the removal not only of infringing videos, but of many which were legally posted and protected under fair use laws.
Among the videos cited by the EFF were clips of teenagers singing Winter Wonderland and an a cappella song performance.
YouTube's takedown policy has long been a source of controversy. TV studios and record companies claim that the site does not do enough to police content, while users and online rights backers such as the EFF blame the site for being too quick to remove original content without first reviewing the video.
Both sides base their arguments on the Digital Millennium Copyright Act (DMCA), a 1998 US law which dictates the terms for posting and protecting copyrighted materials online.
The EFF is also asking YouTube to expedite an upgrade to the content identification system it uses to recognise videos which potentially infringe on copyright.
"It is clear from the Warner Music experience that YouTube's Content ID tool fails to separate the infringements from the arguable fair uses," wrote EFF senior staff attorney Fred von Lohmann.
"And while YouTube offers users the option to dispute a removal (if it's an automated Content ID removal) or send a formal DMCA counter-notice (if it's an official DMCA takedown), many YouTube users, lacking legal help, are afraid to wave a red flag in front of Warner Music's lawyers."
Geoengineering on the sea floor near glaciers would form a new ice shelf to prevent melting
Alterations in capillary blood flow can be caused by body position change
Curiosity rover is in 'normal mode' but not transmitting scientific data back to base
NatWest outage comes a day after Barclays' IT systems shut out customers and staff