The United head coach as ever refused to criticise the officials although the winning Chelsea goal was a little controversial, but he was in no doubt that Leeds had done enough to have brought back at least a draw from Stamford Bridge.
The Whites led in the first half with a penalty of their own, put away by Raphinha, but trailed 2-1 until teenage star in the making Joe Gelhardt scored his first senior goal for Leeds with his first touch after coming on as substitute.
That looked to have given them a deserved point after they had played well in the second half against the title challengers only for the late penalty decision to leave the players feeling robbed.
“I think the fair result would have been a draw,” said Bielsa.
“Both teams played a beautiful game. For us to manage that they didn’t play well was very difficult and to create danger against them also.
“But, in a balanced way, we managed to achieve both things, which wasn’t enough for us to be better than them but we also could not be worse than them."
On the penalty decision that gave Chelsea their win, Bielsa commented: “I never give an opinion, whatever the referee decides is fine with me."
A draw would have been a fantastic result for the Whites given that they had a number of key men missing, including England players Kalvin Phillips and Patrick Bamford, forward Rodrigo and central defenders Liam Cooper, Pascal Struijk and Robin Koch.
But Bielsa was delighted with the players who stepped into the side and had praise too for young striker Gelhardt who took his chance to impress again when thrown on from the bench late on.
He added: “The absences, we resolved them.
“With an added difficulty that we were missing four players in the same sector of the pitch, Robin Koch, Kalvin Phillips, Pascal Struijk and Liam Cooper. The other two absentees were from the centre of the attack.
“But I think Adam Forshaw, Deigo Llorente and Luke Ayling resolved that situation very well. The same with Tyler Roberts, Gelhardt and Dan James.
“He’s (Gelhardt) a player that’s an opportunist. He’s always close to the goal and to have achieved that at this level.
"It was a goal that reflects his qualities and his form. He was in the right place at the right moment. I think those characteristics at this level is important, especially as it was a goal that allowed us to level the game.
“I think it has value that he scored it.”
This was not another of United's failures in London even though the outcome may have been yet another loss in the capital.
There were no thoughts of just sitting back as they gave as good as they got for much of the match and could take a number of positives from their display ahead of another difficult away test against Manchester City on Tuesday night.
They created the first big chance of the game when Raphinha's curling free-kick looked to be heading for the top corner only for home keeper Edouard Mendy to make a superb save in tipping the ball away.
Raphinha had more joy soon after as he put away his second penalty in two matches, after Dan James had been clumsily brought down by Marcos Alonso.
Chelsea hit back when Illan Meslier's pass out put Stuart Dallas under pressure and he lost possession to Alonso, who then combined with Timo Werner to provide a low cross that was swept into the net by England player Mason Mount, with keeper Meslier out of position for some reason.
Chelsea's best spell of the game followed as Leeds threatened to fall apart again as they had done for a similar spell in the previous game against Brentford.
But United survived as Alonso's free-kick went just over, Meslier saved well at his near post to deny Kai Havertz after an incisive move by the Blues and Havertz saw a shot from a corner deflected over.
Leeds started the second half better, but were stunned when a penalty was given against them after Raphinha slid in to challenge Antonio Rudiger inside the area. He won the ball and a corner was given by referee Chris Kavanagh, but VAR intervened and Kavanagh was persuaded to change his mind as there was some doubt about the Brazilian's follow through in his tackle.
It was a harsh decision, but the upshot was Jorginho scoring the first of his penalties to put the home side ahead.
Leeds' reaction to this goal was good, however, as they went on to have the better of the rest of the game.
Raphinha raced clear and denied by a fine Mendy save only to be ruled offside - controversially again - and further good football created a chance for Tyler Roberts, but his shot was comfortably saved.
There was no denying United, however, when good work by substitute Mateusz Klich and Jack Harrison created space down the left for Roberts and his low cross was turned in by Gelhardt shortly after he had come on for Raphinha.
It looked to have given Leeds a creditable draw, but Klich's clumsy challenge on Rudiger saw the big Chelsea defender go to ground easily just inside the box deep into injury-time and Kavanagh's penalty decision was backed up by VAR with Jorginho stepping up to put away his second spot kick.
After the whistle tempers briefly flared with Leeds players, particularly Junior Firpo, wound up by the decisions that had gone again his side. They could consider themselves unlucky, but should take confidence from their efforts against such a top side.
(Mount 42, Jorginho 58 pen, 90+4 pen)
Leeds United 2
(Raphinha 27 pen, Gelhardt 83)
Saturday, December 11, 2021
Chelsea: Mendy; Azpilicueta (Christensen 74), Silva, Rudiger; James, Jorginho, Loftus-Cheek, Alonso (Lukaku 87'); Mount, Werner (Hudson-Odoi 74); Havertz.
Leeds: Meslier; Dallas, Llorente, Ayling, Firpo; Forshaw; Raphinha (Gelhardt 81), Shackleton (Klich 59), Roberts, Harrison; James (Cresswell 87).
Referee: Chris Kavanagh