Tom Barkhuizen gave PNE the lead with 16 minutes to go before the visitors equalised in the 87th minute, with the game becoming a much more open and frantic encounter.
Bielsa felt that both sides could have won the game, but neither could quite arrest the parity between two well matched outfits and the direction the game was going in.
The Argentinian said: “Until they scored, the match had a direction that was difficult to change.
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“After the Preston goal we multiplied our efforts to try and score. After we managed to score, we could have won the match.
“But we cannot ignore that after they scored, they had some chances to score again.
“Maybe they could have won the match.
“Until they scored, the match was completely for us.
“In this period, until we drew the match, we could have received the second goal or we could have a draw as we did.
“After the draw, we had a sensation that we could have won the match as well.”
Alex Neil had changed tact to previous home games, instead making preparations for Leeds’ style and not looking to dominate the game.
Bielsa acknowledged the threat that North End posed, despite having less of the ball, with PNE looking a threat on the break, especially in the second half.
“What is clear is that the opponent doesn't need to command the match to create danger,” Bielsa said.
“We dominated a lot, we commanded the match, we created a lot of danger, but it is difficult for us to unbalance the match.
“When the match ends in a draw, we had a lot of chances to score and it seemed difficult today to score.
“After they scored, we continued to attack and there were some chances.
“Linking my job here in Leeds, we could write a book about these kinds of situations.
“I have explained this situation a lot of times and I always try to add details to make it a little bit different.
“But it is the same situation.”