The midfielder was gutted after losing Wednesday evening's European final in the Romanian capital, and felt Atletico's first goal cost the Basque giants the game
A Radamel Falcao double gave the Vicente Calderon outfit a comfortable lead at half-time, before Diego put the match to bed after the interval, much to the dismay of Herrera.
"We're devastated. I suppose with the passing of time we'll see it differently, we'll feel proud. But right now there's only pain," the midfielder was quoted as saying on the official Uefa website.
Herrera then went on to claim that Falcao's early opener cost Bilbao as they never managed to get back into the game once Diego Simeone's side went 1-0 ahead.
"The first goal did a lot of damage and we weren't able to get back on track."
Bilbao will be looking to return to winning ways on Sunday when they take on Levante, before facing Barcelona in the Copa del Rey final on May 25.