Leeds suffered heartbreak at Elland Road after seeing a 2-0 aggregate lead slip away with the Derby prevailing 4-2 on the night and 4-3 on aggregate.
It was a bitter blow for Leeds and Bielsa, who had looked good bets for automatic promotion until faltering at the business end of the season, missing out to Sheffield United.
The Yorkshire side had won all three previous meetings with Frank Lampard’s men this season but in the most important one of all, they came short.
It had been a different story leading up to half-time after Stuart Dallas had put Leeds 1-0 up midway through the first-half.
But right on the stroke of half-time, substitute Jack Marriott pulled Derby level after a mix-up in the home side’s defence.
And the Rams turned the tie on its head after the break through Mason Mount and a Harry Wilson penalty, only for Dallas to drift in and fire Leeds back level on aggregate.
Leeds defender Gaetano Berardi was then sent off for a poor challenge on Bradley Johnson before Marriott won it late on with a composed finish.
There was still time for Derby defender Scott Malone to join Berardi in being dismissed after collecting a second booking in time added on.
“If the club offers me the possibility to carry on I will listen to the proposal”
For Leeds, who finished third in the table, defeat means their spell outside the top flight will stretch to a 16th year.
Bielsa, who joined at the start of the season, will now have to decide whether his future remains at Elland Road but says he will listen to what the club want to do going forward.
The former Argentina manager is claimed to have a break clause in the contract he signed which will kick in if Leeds are not promoted.
“If the club offers me the possibility to carry on I will listen to the proposal,” Bielsa said.
And the 63-year-old was left to rue missed chances from his team that ultimately sent Derby to Wembley where they will play Aston Villa in the final.
“It’s a painful situation and we are very disappointed,” he added. “It’s not necessary to analyse, during the season the games that could have allowed us to find a solution to all possibilities we couldn’t make a different for those games for the same reason as today.
“In the first half we should have finished with two goals more, but we finished [level]and in the second half it’s a game that broke immediately.
“The chances of the opponent ended in goals and ours not. It’s meaningless explaining that we had as many chances as the opponent in the second half and in the first we made more, it should have made a difference.”
It remains to be seen what backing Leeds can offer Bielsa over the summer to mount a fresh promotion bid.
LEEDS UNITED boss Marcelo Bielsa says he will listen to offers but has refused to commit his future to the club after seeing his team crash out of the Championship play-offs in the semi-final to Derby.