Leeds’ 100 per cent record was ended at the Liberty Stadium as Bielsa’s side were twice forced to recover from a goal down to earn a point through an 80th-minute goal from former Swansea midfielder Pablo Hernandez.
Bielsa’s pre-match plans were disrupted by an injury to captain Liam Cooper suffered in the warm-up, forcing United’s head coach to play Jamie Shackleton at right-back, and a torrid start saw Kalvin Phillips’ 100th appearance for United end with his substitution after 28 minutes.
Oli McBurnie - the Leeds-born striker who was heavily linked with a move to Elland Road at the start of the summer - struck for Swansea on 24 and 51 minutes but Kemar Roofe’s first-half equaliser and Hernandez’s late intervention staved off a first defeat of the campaign.
Bielsa said: “We didn't defend very well and this did not allow us to dominate the game with regularity. For the first half Swansea dominated the game. It took us almost 25 minutes to get into it.
Leeds United fans react to 'battling' Swansea City draw“In the second half we had more stability. After 2-2 we dominated the game. We could have won this game and we could have lost it too. It was a nice game to watch but there are some important aspects we have to correct.
"To attack, you have to defend well. But the offensive performance was good enough. There were some good things we did. From my point of view, the draw is a good result, a fair result."
Leeds sit at the top of the Championship after four games, unbeaten with 10 points, but Bielsa insisted the table was insignificant less than a month into the season.
“What we’ve played so far is just a small part of the competition,” he said. “I know it’s an important position to be first in the table but it doesn’t mean a lot.”
Leeds are facing a shortage of centre-backs after losing Cooper to a hamstring strain. United, who were already without Pontus Jansson against Swansea, are assessing their club captain and waiting to see if Jansson will recover from a back injury in time for Saturday’s trip to Norwich City.