The Whites had to settle for their third draw in five games after letting an early lead given them by Raphinha slip to draw 1-1 at St James' Park.
It means that they are still winless in the league this season and so are their hosts, but both played their part in a cracking end to end contest in which it was a surprise there were only two goals.
"We should have won," said head coach Bielsa.
"We had a lot of opportunities to score and there were also a lot of options where they didn’t end up in danger, but it would have been easy to convert to danger.
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“It is true that the opponent also had chances. Less than us and within a transmit that was different.
“We dominated the game and they counter attacked. But, I insist, given the chances we had we should have won the game.
“I also would have hoped we would have reduced the amount of chances that the opponent created.
“That would have established a bigger margin between the two teams."
Bielsa admitted injuries were beginning to take their toll on the team. With two centre-backs already injured and one suspended United lost stand-in central defender Luke Ayling to injury late on. Playmaker Raphinha also came off with a knock to leave the side with just one recognised winger as Jack Harrison missed the match through illness.
"We have four centre-backs and Ayling is a fifth. If we have to resolve the absence of four of them it will be complicated," added Bielsa.
"The same with the wingers. We count on James, Harrison, Raphinha and Summerville. To lose two of them will make it difficult to resolve.
"I always have confidence we will find the solutions."
Leeds got the start they were looking for as they tried to get their first win of the campaign with Raphinha's clever angled cross sneaking in at the far post after Rodrigo's equally clever dummy allowed the ball to run in the box.
More goals almost immediately followed as Mateusz Klich and Raphinha were both denied by home keeper Karl Darlow.
Miguel Almiron hit a shot wide at the other end and Illan Meslier was forced into his first save as Newcastle produced a good move that resulted in a Joelinton effort.
The pace of the game continued and Klich was only denied by a fine Darlow save after a swift attack involving Ayling and Raphinha.
Both sides went close with shots from the edge of the box, Kalvin Phillips seeing his effort go inches wide and Newcastle' Matt Ritchie hitting the post.
The visitors should have had a penalty as Dan James was tripped inside the area, but their big shouts fell on deaf ears with referee Mike Dean and the VAR man who failed to intervene although replays showed it was a clear cut foul.
Other promising positions for the visitors were wasted and they paid the price as their opponents equalised just before half-time with Allan Saint-Maximin showing some superb skill to run past several defenders before planting a well struck shot past Meslier.
The end to end pattern continued right into first half added time as the hosts were denied by a good tackle on the edge of the Leeds box and like lightning the Whites broke as Junior Firpo made ground down the left and found Raphinha unmarked in the area.
The Brazilian for once was not so impressive as he took too many touches, but when his shot was blocked and the follow-up by James was also blocked the ball invitingly back to Firpo only for the summer signing to blaze over with the goal gaping.
The second half could not match the first for thrills, but there were still decent chances for both teams.
Darlow had to be alert to tip the ball over after Jamal Lascelles had headed it towards his own goal from James' cross while Meslier also saved well from the ever dangerous Saint-Maximin.
Leeds lost a little of their threat when Bielsa changed both his wingers, Tyler Roberts coming on to play on the right and 19-year-old Crysencio Summerville making his first team debut. Neither were able to make much impact.
But the Whites did create one golden chance as they went down the middle and Rodrigo - who had a much improved game at number 10 - sent Patrick Bamford clear only for the recently England capped striker to be unable to beat Darlow with a right foot shot.
Saint-Maximin continued to be the chief threat for the home side and he saw two shots saved by Meslier.
Newcastle failed to make much of several corners and Leeds were in the end grateful to take a point as they finished the game with Phillips in the back four.
The injuries certainly disrupted them in the second half and could force Bielsa' hand on what kind of team he will now pick for the next game, a Carabao Cup game at Fulham next Tuesday.
Newcastle United 1
(Saint Maximin 44’)
Leeds United 1
Friday, September 17, 2021
Newcastle: Darlow; Clark, Lascelles, Manquillo (Krafth 81); Almiron (Fraser 62), Hayden, Willock, Logstaff, Ritchie; Saint-Maximin, Joelinton (Murphy 90),
Leeds: Meslier; Dallas, Ayling (Shackleton 89), Cooper, Firpo; Phillips; Raphinha (Summerville 67), Klich, Rodrigo, James (Roberts 61); Bamford.
Referee: Mike Dean