Bilbao headed into the second leg of their quarter-final clash with a 4-2 advantage from last Thursday, and eventually booked their final-four spot after a 2-2 draw.
But while many believed the La Liga outfit were always favourites to progress, Bielsa insists it was never a given.
"To say it [the game] was more difficult than expected is to think that it could have been easy, and we never thought that this rival was going to be easy," the Argentinean said in his post-match press conference.
"The draw was fair, it was positive result."
"The beginning of the game was not comfortable for us. As time went on, we played better. Reacting quickly was key to stop the momentum of Schalke."
"At the start of the second half we did not count on them scoring a goal. After our second equaliser, we played well. The last half-hour from my point of view was good."
Bilbao will now meet Sporting Lisbon in the semi-finals, an encounter Bielsa is looking forward to.
"Portuguese football is very attractive and I am happy to compete with them [Sporting] as they belong to the hierarchy of football in the country," Bielsa added.
Bielsa was also asked at his post-match press conference about speculation linking him with a move to Inter Milan, but said only: "In these kind of issues it seems prudent to speak of bare facts and not hypothetical situations."
Bilbao are next in action on Sunday when they entertain Sevilla in La Liga.