Bale missed Sunday's victory, but was allowed to join the Wales squad this week - despite Perez's hesitation.
However, after scans, Bale was ruled out of Wales' international programme with a calf strain. FAW doctors believe he faces another month on the sidelines.
Real, including coach Zinedine Zidane, had insisted Bale was rested for the Espanyol game and his injury problems weren't serious. The fact that Wales has laid bare the extent of the latest setback has infuriated Perez.
The president had attempted to cloak Bale's problems and with everything now out in the open he is furious with the situation.