Bielsa assumed responsibility for being unable to overcome Cardiff's renowned aerial and set-piece prowess and would not blame his players or the absence of Liam Cooper, the club's most physically dominant defender.
The Argentine felt some of Leeds' attacking play was the best they have produced, as they roared into a 3-0 lead.
Patrick Bamford scored twice, one of which a penalty he himself won, after Helder Costa opened the scoring on six minutes.
And United created other chances to hit the net, but the likes of Pablo Hernandez, Luke Ayling and Stuart Dallas were wayward with efforts in and around the area.
"It's very difficult to explain," said Bielsa.
"The only explanation we can try would be try to value how we conceded the three goals, the opponent arrived to our box with set pieces or long throw ins or crosses, corners. Of course we knew that, because we know this in the Championship is an important fact. The other point is we had a three-goal difference, we scored three times and missed 10 chances and after we had another 10 situations that should have finished with more danger.
"But when you score three goals you cannot criticise why we didn't score five goals. We had moments in the match, we played the best football so far but this is something different in this analysis, the question is how, with a difference of three goals with an opponent that didn't surprise us with their resources?"
Bielsa was adamant that the nerves he has seen before from Leeds in a difficult spot were not on display as Cardiff fought their way back into the game.
"It wasn't what happened today, the team was calm, then 3-1, 3-2 and 3-3, our team was calm, was in control. But clearly we conceded three goals that we cannot explain," he said, before taking the blame for not being able to legislate for Cardiff's presence at set-pieces.
"The manager knows the characteristics of the opponent, we demand the same kind of response from our side so the manager is engaged with this situation," he said.
"When the manager knows something is coming and didn't achieve to resolve it, they lost a centre-back with good aerial play, but our problem in this sense didn't disappear. Everyone knew before the game this was the big resource of the opponent. If one team had 30 chances to score or 25 and the opponent [only] with throw-ins, corners, set-pieces, with less elaboration, less building, they draw the match, we cannot compare both things. What we have to do is think that we knew what was going to happen and we couldn't resolve it. So I clearly feel that the preparation for this match wasn't enough.
"I value Liam [Cooper] but I cannot say that we drew the match because he wasn't on the pitch. Of course it is easy to say because everyone will understand, one experienced player could avoid this situation. But I don't think that, I think more in what I said before. Knowing the difficulty I couldn't prepare the team properly to avoid this."
Bielsa also absolved his substitutes of blame for what transpired in the final 10 minutes and the two goals that Cardiff scored, despite being down to 10 men by that stage.
Ultimately, he concluded that this was not a result that he could explain.
"You have some results you can explain, you have others that are more difficult to explain. We cannot explain this result, it wasn't possible to draw this match."