Although Illan Meslier made a number of good saves, the Whites created problems for their visitors too, Edouard Mendy tipping a Tyler Roberts shot onto the bar in the first half, Diego Llorente seeing a goalbound effort deflected off target in the second.
"Evidently we played against a team that is superior to ours," said Bielsa.
"But in the second half especially, the first half less, we did what was necessary to play a balanced game and at the end of the game the chances both teams had were similar. It's true the superiority they showed in the first half was greater than the superiority we showed in the second half, but to be able to play a game like we did today we have to make an enormous effort."
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Bielsa, without captain Liam Cooper through illness, was particularly pleased to compete for 90 minutes and create a similar number of chances against a side with such attacking riches - Chelsea began the game with Hakim Ziyech, Christian Pulisic, Mason Mount and Kai Havertz in their forward line and later brought on Timo Werner and Callum Hudson-Odoi, while Olivier Giroud stayed on the bench.
"What makes a team like Chelsea so fearful is that for the four positions in attack, the two wide men, the striker and the one that plays behind, they are able to count on two players for each of their positions," he said.
"The most difficult thing in football is the positions in attack, they're the players most substituted. When you have four of those on the field and four more to be able to put on, it's not easy to face these types of teams. We made a big, big, big effort so the game wouldn't become unbalanced. It is with a slight predomination in the second half, and a more clear dominance from them in the first half. But the offensive production of each team was similar and this is very difficult to achieve. If you take for example the last game they played before they played us, the first proper chance Chelsea conceded in that game was in minute 90. So for us to have provoked five or six chances at goal has its merit."
A first half injury to Patrick Bamford gave his replacement Rodrigo a chance to increase his match fitness and although the Spaniard was himself substituted late on by Mateusz Klich, Bielsa was more than content with the attacker's display.
"The period in the first half and the period of the second half he played, the efforts he made were superior physically to the efforts he's capable of after 40 days out injured. I value a lot how he was able to perform in the 50 minutes or so he played. Although he is healthy and physically fit, the competitive rhythm he needs is still not there yet.
"The contribution Rodrigo made was above what he's actually capable of doing at the minute. More than apologising to him I have to thank him for the contribution he made while he was on the pitch, because I insist the contributions he made are not corresponding to where he's at on his return."
Bielsa had no information on the extent of Bamford's injury before he spoke to the press, but made a point of praising Tyler Roberts for his performance in both the number 10 and lone striker roles.
The youngster was unlucky not to score and created moments of danger for Leeds in one of his best games of the season so far.
"The game today showed an evolution from Tyler in his game, as a number nine as well as a number 10," said Bielsa.