Speaking after the match, Bielsa explained that the substitution was not his call, confirming Muslera requested to leave the pitch following his difficult first-half display.
"I didn’t make it [the decision of substituting the GK], that’s a decision Muslera himself made," Bielsa admitted.
Muslera later accepted full responsibility for his performance and apologised to both his team-mates and the Uruguayan supporters.
"I've never been one to hide, but to face the music," he said, as quoted by Mundo Deportivo. "This is the most direct way to speak to the Uruguayan people. I never imagined I would suffer so much with this sport. Especially with all the work I put in, how I prepared.
"I told the lads in the locker room at the end of the game, when they were a bit calmer, 'Today it's my turn... I haven't had a good World Cup'. I apologized to them and to all Uruguayans, although it's too late now."