Leeds came into the game with a one-goal lead from their victory in the first leg at Pride Park and Stuart Dallas gave the Whites the ideal start to the second leg with a goal after 24 minutes.
However, two goals from Jack Marriott, one from Mason Mount and a penalty from Harry Wilson secured Derby a 4-2 win and a place in the Championship play-off final against Aston Villa at Wembley.
If Leeds had secured promotion to the Premier League, either through automatic promotion or the play-offs, then Bielsa’s contract would have automatically been extended for another season.
But now the Whites have extended their exile from England’s top division for a 16th year, Bielsa’s future at the club is up in the air.
Leeds majority owner Andrea Radrizzani has made it clear he wants the 63-year-old Argentine to stay on for another year and the former Argentina and Chile boss hasn’t yet ruled out having another go at winning promotion.
“As you can imagine, it’s not convenient to talk about this right now,” Bielsa said after Leeds lost 4-3 on aggregate to Derby.
“This process, you know about it, is that if the club offers me the possibility to carry on I will listen to their proposal.
“What the players offered to the club this season will be valued over time.
“The fact that we couldn’t reach the goals we were so close to leaves a feeling of disappointment but you can have another perspective about it.
“I already mentioned that it would be very difficult to see these players play at the same level in another season.
“We had so many difficulties but I have to say that we had the conditions to finish first or second (in the table) and all the conditions to be the best team in the play-offs.
“We couldn’t finish first or second and we couldn’t reach the final.”
Few would have predicted such a frantic night at Elland Road that saw six goals, two red cards, a penalty and 11 bookings.
Victory for the Rams meant they are the first team ever to lose the first leg of a Championship play-off semi-final at home and then go on to reach the final.
After the game Derby boss Frank Lampard admitted he wasn’t completely confident his side were going to achieve a historic comeback win.
“I’d be naive to say I totally believed we could come back but I had belief in the players,” he said.
“As a manager, the pressure is more intense than as a player. I wanted this so badly, you worry you want it too badly. I’m very proud.
“We’ll be underdogs in the final and tomorrow we start again.”
As for Bielsa, he reflected on decisions he made in a game he thought was there for taking.
“Obviously there are mistakes that prevented us from reaching our goals,” he added.
“And when you can’t reach something that was reachable, it always puts doubt on the head coach.”