United dropped into the bottom three of the Premier League in the process on a see-saw afternoon against the Hammers, who scored a late winner in a 2-1 triumph courtesy of Michail Antonio.
The former Sheffield Wednesday player had earlier been involved in controversy after the Hammers saw a 54th-minute 'goal' ruled out by VAR.
Tomas Soucek had netted the loose ball after Leeds keeper Illan Meslier - outstanding on the day - was illegally challenged by Antonio, who caught him with a flailing arm with the Frenchman receiving lengthy treatment following the incident. Antonio was booked but remained on the pitch.
Earlier, Leeds had led thanks to a superb 19th-minute strike from Raphinha, who was later substituted with just over twenty minutes to go shortly after the Hammers equalised, with Bielsa confirming that the Brazilian told him that he was feeling the effects of a knock sustained in the recent draw at Newcastle.
West Ham levelled in fortuitous fashion when Jarrod Bowen cut inside and saw his shot take a wicked deflection off Junior Firpo before flying past Meslier, who had earlier made four fine saves.
The Londoners pushed for a winner in the final quarter and it arrived when Declan Rice's pass found Antonio, who got the better of Jamie Shackleton before firing past Meslier to break Leeds hearts and extend their unbeaten away league sequence, stretching back to April.
It took Leeds's winless league sequence at the start of 2021-22 to six matches, equaling identical runs at the start of 1935-6 and 1951-2.
Bielsa, whose side welcome Watford next weekend, said: "The two teams had different realities. In this case, they found the triumph. I don't think we deserved to lose. I imagine the opponent's manager thinks they deserved to win. When a team finds themselves in a good moment, they obtain these recompenses.
"When a team accumulates negative results, they don't find a lot of things they deserve.
"When you conserve a result, we stopped (in the second half) doing some things that are necessary to avoid losing what you obtained.
"Responses like this are sometimes natural. Trying to hold onto what you've got and forgetting the path that led you there. We spent too much time defending and not enough time in the opponent's half. When you defend too close to your goalkeeper, it's likely their chances increase."
On the substitution of Raphinha, who consistently threatened West Ham alongside Rodrigo - while at the back, teenager Charlie Cresswell had an excellent league debut - Bielsa added:
"He let us know it was becoming difficult for him to stay on the pitch. "Throughout the whole week, he was recovering from the knock at Newcastle. He played a great game as long as he could stay on the field."
Bielsa confirmed that Adam Forshaw was not involved on the bench due to a thigh injury and will face a short spell out.
"He had a tear in the posterior part of this thigh," the Argentine said.
"With a muscle, they consume a month's time. Forshaw makes enormous efforts not to injure himself, but after two years out it's hard."