The Spanish international, a £26m club record signing last August, was an unused substitute in the entertaining encounter with the Blues, which saw the hosts come from behind twice to register their first point of the season.
On the previous Saturday, Rodrigo had been substituted at half-time in the 5-1 loss at Manchester United.
Bielsa revealed that the decision to name the 30-year-old on the bench was more to do with the fact that he had been hindered by a ‘slight muscular issue’ earlier in the week.
Bielsa, whose side secured a point courtesy of a brilliant 72nd-minute strike from Raphinha, who scored for the third successive match against Everton, said: “During the week, he had a slight muscular issue of which he recovered quickly.
“If that had not happened, he would have been our offensive midfielder in the game today (on Saturday).
“I have a lot of confidence in the qualities of Rodrigo. During his holidays, he did physical work that was very important and during the six weeks of pre-season, he’s the player who shone the most in those weeks.
“I have a lot of hopes for him that this season he is going to show all the qualities that he has.
“In the game, I opted for (Mateusz) Klich and Tyler (Roberts). He could have played, that is why he was a substitute, but I preferred two other players to come on instead.”
Saturday’s game saw United’s marquee summer signing Junior Firpo handed a full debut and the ex-Barcelona player endured a difficult baptism in front of a crowd of just over 36,000 spectators at Elland Road.
It was an afternoon when Leeds struggled defensively, with impressive Everton winger Demarai Gray posing plenty of problems in particular.
Going forward, the axis on the left between Firpo and Jack Harrison struggled for fluency, but Bielsa believes that patience is required in that regard and is confident that the on-pitch relationship will grow in time.
On the impact of Firpo and Harrison, Bielsa, who confirmed that German international Robin Koch missed the game with a minor pelvic injury, added: “It is a question that comes with the answer included in the sense that they are not producing what they can with regards to the quality that they have.
“Firpo is a highly-technical player and he has an explosiveness to move and that should mix well with Harrison’s characteristics, but we cannot think that the (relationship) between them is going to happen rapidly and spontaneously.”
On a venerated occasion which saw home supporters return en masse to Elland Road for the first time in 532 days, Leeds displayed character, resolve and quality to haul themselves level on two occasions against an Everton side who caught the eye in their first away fixture of the tenure of Rafael Benitez.
The first-ever managerial meeting between Benitez and Bielsa proved a match to savour on a day when both sides produced 17 shots on goal.
Bielsa acknowledged that his side struggled to carve out meaningful clear-cut chances in contrast to Everton, but he professed satisfaction in the reaction of his side, seven days on from a potentially psychologically damaging defeat at Old Trafford.
Bielsa commented: “The game was a big test for the team and this was multiplied because we were behind twice. To have been able to draw the game and to have dominated it for so many moments, they 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 fewer less chances at our (goal). We played a game against an opponent that did not need to dominate us to create chances.”
“We didn’t start the second half well. And after the goal, there were disconcerting moments as a product of the effect of having gone behind once again.
“It is a situation which is normal in football when a team is losing but not because of that, should we run the risk of conceding more goals. That’s to say that those moments after 2-1 were the most fragile of the team.”
Raphinha’s strike would restore parity in glorious fashion in an entertaining game which was befitting of a grand occasion when a full house of fans returned to Elland Road after an absence of 17 months.
Speaking for many, Leeds’s talisman midfielder Kavlin Phillips, who returned to the starting line-up, said: “It has been amazing having the crowd back.
“The fans showed how much they have missed us and we have really missed them. Having a full crowd is like an extra man.”