Bielsa's side, humbled 5-1 at Manchester United on the opening day, hit back twice to earn a deserved point in their first top-flight game with a full house at Elland Road in 17 years.
Dominic Calvert-Lewin's first-half penalty was cancelled out by Mateusz Klich before the break and after Demarai Gray had restored Everton's lead, Raphinha raised the roof with a thumping equaliser.
"The game today was a big test for the team and this was multiplied as we were behind twice," Bielsa said.
"To have been able to draw the game and to have dominated for so many moments, they are aspects to value."
It was a typically thrilling Leeds encounter as the home side set about restoring lost pride in front of a crowd of 36,293 in their accustomed dynamic style and Everton always dangerous on the counter-attack.
Bielsa's satisfaction at seeing his side back in the kind of form that lit-up the Premier League last season was tempered by some disappointment.
"Given the amount of minutes that we dominated, we should have created more chances at goal and we should have conceded less chances at our goal," he said.
"We played against an opponent that didn't need to dominate us to create danger."
Everton have taken four points from boss Rafael Benitez's first two games in charge after their 3-1 opening-day home win against Southampton and the Spaniard accepted a share of the spoils was a fair reflection.
"They were pushing from the beginning and we reacted well, especially in the second half," the former Liverpool, Chelsea and Real Madrid manager said.
"We had the chance to score the third goal and maybe we would have been talking about something different.
"Overall, they were pushing, we were reacting and after, when we had good transitions, everything could change, but I think maybe it's fair."
Benitez, who was locked in a long conversation with Bielsa following their post-match television interviews, was impressed by his side's resilience in the face of a raucous, partisan atmosphere.
"We could see how good our fans were for us (against Southampton) and we could see today how good their fans were for them," he said.
"Our mentality, the way that the team were battling against all the things around and I'm really pleased because of that."