The Whites played in front of a packed Elland Road for the first time since March 2020 and amid a feverish atmosphere came from behind twice to take a point.
Mateusz Klich cancelled out Dominic Calvert-Lewin's penalty and Raphinha belted in a wonderful shot after Demarai Gray put the Toffees ahead again.
Elements of the performance, including the point, pleased Bielsa.
"The game today was a big test for the team," he said.
"This was multiplied as we were behind twice. To have been able to draw the game and to have dominated for so many moments are aspects to value. But given the amount of minutes that we dominated we should have created more chances at goal and we should have conceded last chances at our goal. We played against an opponent that didn't need to dominate us to create danger.
"Our goalkeeper made two interventions that we valued as a goal in our favour today and allowed us to get the draw."
Leeds' dominance was tested in the second half, particularly after Everton went ahead, goalkeeper Illan Meslier called upon to make a number of important stops to keep Leeds in the game and allow them to regain their footing.
A double swap from Bielsa helped matters, with Jamie Shackleton keeping Gray quieter and Stuart Dallas able to drive the team on from the left hand side of a midfield three.
"We didn't start the second half well and after the goal there were disconcerting moments, product of the effect of going behind once again," said Bielsa.
"It's a normal situation in football when a team is losing. That's to say those moments posterior to the 2-1 were the most fragile of the team."
The second half change brought Shackleton and Tyler Roberts on to replace Klich and Junior Firpo, whose on-field relationship with Jack Harrison Bielsa says needs time to develop.
"It's a question that comes with the answer included in the sense that they're not producing what they can with regard to the quality they have," he said.
"Firpo is a highly technical player and he has an explosiveness to move and that should mix well with Harrison's characteristics.
"We can't think the game between them is going to happen rapidly and spontaneously. I think there's going to be progressions until we finally get what we expect."
Referee Darren England tried to let the game flow, particularly in a physical opening that saw Leeds give Richarlison a difficult time. The light touch officiating seen at the Euros has not gone unnoticed in the Premier League, nor has it escaped Bielsa's attention but he is unable to say if it benefits Leeds' style.
"It's true that the refereeing is more lenient now," he said.
"I wouldn't be able to tell you if that favours our style of play. It allows us to recover the ball more easily because there are fouls that are not whistled. It doesn't allow some of our attacks to develop because you need a higher dosage of speed. I think adding and subtracting in the end there is not big differences."
The atmosphere added mightily to the occasion, Elland Road exploding for each of Leeds' goals having been filled with a raucous din from around 2.45pm.
Bielsa was delighted to see the full return of supporters to the stadium.
“The public is always a stimulus and the presence of the spectators is very important," he said.
"It made us very happy and it was very emotional to play in front of them again. The contribution of the fans is always something that makes the game grow."
Leeds were without centre-half Robin Koch who Bielsa said was suffering from pain in his pubis which had not abated in time for him to play a part in the game.