Despite the familiar domination by the Whites, evidenced by their 70 per cent possession, they failed to find the back of the net and fell victim to a Wayne Routledge goal in the 90th minute to see their unbeaten Championship record ended.
It meant Leeds have now only won of their last seven home games going back to last season and they have conceded three goals from corners in their first four home matches this season.
But the Leeds head coach declared himself happy enough with his team's start to the season as they have collected 13 points from the first six matches before the oncoming international break.
Bielsa said: "The individual performance of the players was positive.
"Our players played a little under the limit that they have. But we defended well. We created enough chances to deserve two or three goals.
"The chances that the opponent team had was restricted to corners, more from the second ball from the corners.
"So honestly we can’t criticise this point of the team.
"We had 70 per cent of the ball with a very good balanced referee, with an opponent that tried to play and the team created 12 or more chances at goal.
"We had high possession of the ball and we attacked with calm."
On Leeds' start to the season Bielsa added: "We have lost one game that we could win.
"We lost one game that we could win perfectly.
"We have lost five points playing at home so then you have enough space you can be a little bit disappointed.
"We cannot criticise the style of the team who play, but we were creating conditions to win all six games."
Leeds reverted back to their regular league line-up, with skipper Liam Cooper back in central defence, and made a sharp start.
Swansea came to play, but were hustled out of their stride as United's pressing game was seen in full effect.
As has been the case in home games, however, Leeds domination was not turned into goals in the opening half.
Gjanni Alioski hit two early efforts, one over and one that produced the first save from visiting keeper Freddie Woodman.
Patrick Bamford was next to be denied by Woodman with a near post effort following a good run and low pull back by Jack Harrison.
Bamford should have scored in the 15th minute when free in the area to meet a cross by Stuart Dallas, but he sent his header wide.
A more difficult header soon after for Bamford met with the same result.
Swansea finally got a foothold in the game as one-time Leeds player Matt Grimes sent a free-kick into the side netting.
Leeds were back on the attack as a lovely move ended with Adam Forshaw sending a chip just over following Mateusz Klich's pull back.
Home keeper Kiko Casilla was forced into his first save just before the break when Grimes got a shot in from outside the box after Bersant Celiuna's free-kick had seen the ball bounce back to him off a defensive wall.
But the closest to a first half goal came in injury time when Cooper rattled the crossbar with a header from a corner and put the rebound over.
More domination from United followed after the break as Hernandez saw a shot from the edge of the box well saved by Woodman.
A reluctance to shoot saw further promising opportunities wasted and Bielsa threw on Eddie Nketiah from the bench in place of Bamford.
Within a couple of minutes the Arsenal loanee raced onto Harrison's first time pass in behind the Swansea defence only to shoot over.
Hernandez then seemed to want to walk the ball in and when it broke to Harrison his shot was well blocked as another chance went by.
Another opportunity followed for Hernandez, but he shot over after a great run and pull back by Nketiah found the Spaniard in space on the edge of the area.
Swansea finally created a chance themselves as substitute Sam Surridge headed over at the far post, but United had a great opportunity to go ahead when Nketiah got on the end of a Dallas chip in only to send his header into the side netting.
With the game seemingly heading for a stalemate the visiting struck their winner right at the start of injury time. A corner was not cleared several times and Routledge's shot sneaked into the bottom corner of the net.
There was no time for a comeback from Leeds and they were staring at their first defeat of the season.
Leeds United 0
Leeds: Casilla, Dallas, White, Cooper, Alioski (Douglas 83), Phillips, Hernandez, Forshaw, Klich (Costa 71), Harrison, Bamford (Nketiah 61).
Swansea: Woodman, Roberts, Van Der Hoorn, Rodon, Bidwell, Fulton, Grimes, Ayew (Byers 85), Dhanda (Routledge 63), Celina, Baston (Durridge 63).
Referee: Darren Bond.