At the end of one of the hardest weeks of his Elland Road tenure, by his own admission, United overcame adversity to claim a share of the spoils in stoppage time, thanks to a 94th-minute penalty from Rodrigo.
It owed plenty to the outstanding impact of substitute Joe Gelhardt, with fellow replacement Crysencio Summerville also producing an excellent cameo from the bench.
Summerville had replaced United's star turn Raphinha, who hobbled off in worrying fashion in the 54th minute.
Leeds were trailing to a 10th-minute opener from Hwang Hee-Chan and looking out of sorts amid a subdued atmosphere.
But the hosts, with just one win from eight league matches this term, refused to feel sorry for themselves and pushed for an equaliser in the final quarter with home fans buying into their spirit and heart in testing circumstances without the likes of Raphinha, Kalvin Phillips - an unused substitute on the bench - Patrick Bamford and Luke Ayling.
Bielsa kicked every ball from the sidelines and his side were rwwarded late on when Rodrigo converted from the spot after Nelson Semedo's foul on Gelhardt.
Bielsa said: “We deserved something more than the draw. Apart from some things at the start of both halves, we had the control of the game.
"Progressively we started to get closer and closer to the goal and to have won the game would have been more in accordance with what happened on the pitch.
"It was a step forward. But compared to the game last week, it was a performance which outshone it and this performance looked a lot more like the team we are capable of."
On the impact of Gelhardt, he continued: "In the initial minutes when he came on it was difficult for him to get on the ball and in the 15 minutes he was causing danger constantly. Not only with the penalty but a few occasions he could have scored.”
Bielsa said that he has no current update regarding Raphinha, who went off following a challenge from Romain Saiss.
"He received a knock and we don’t know the extent of the injury yet,", the Leeds head coach added.