Following a disappointing first-leg display last week which saw Bilbao held to a 0-0 draw by their lower-league opposition, Bielsa's men cruised to a comfortable win at San Mames with goals coming from Markel Susaeta, Ander Herrera, Gaizka Toquero and Mikel San Jose.
And following the disappointment of two consecutive goalless draws against Albacete and Getafe, Bielsa was relieved to see his side get back to winning ways in emphatic fashion.
"This game was an exception because the level we reached was not similar to what we had done in our recent matches," Bielsa told Marca.
"The attack was effective and varied and we had many goal situations distributed amongst our offensive players."
Bilbao will now play Real Mallorca in the quarter-finals, and are back in action on Sunday when they entertain Levante in La Liga.