On the scoreboard, Phil Jagielka's 50th-minute own goal was all that separated the Whites from the Blades, despite some excellent football from Bielsa's side.
Jack Harrison scored the opening goal and it was his cross Jagielka diverted either side of Ben Osborn scoring the visitors' only shot on target.
Stuart Dallas skimmed the junction of post and crossbar with a second-half shot, and Leeds had a host of other chances without putting the game to bed.
“We won only by one goal,” said Bielsa. “When the opponents sees there is only a one-goal difference they insist on attacking their opponents' goal a lot but we had sufficient amount of chances to score more goals and especially we had many dangerous situations that didn't end in shots that would have increased the options to score more goals.
“It's very difficult in the Premier League to imagine a comfortable victory, at least for us.”
Harrison formed had dipped a little in 2021, perhaps as a result of fatigue in such a hectic schedule, but he continued the improvement shown at Fulham in the last game before the international break.
“In the last two games he's had a bigger increase in his performance (levels),” said Bielsa. “Today he had a lot of influence, he was decisive and in the game against Fulham too.
“When he manages to be at his best version he has a big influence on our offensive play.”
Bielsa had written in his programme notes about wanting to mark the first game since Peter Lorrimer's death with a victory. There was also a minute's applause before kick-off to mark the 21st anniversary of fans Chris Loftus and Kevin Speight whilst in Turkey to watch their team play Galatasaray in the Uefa Cup.
“Victories always generate happiness and optimism and when we lose someone it always generates sadness and memories,” reflected Bielsa.
“It's very difficult for a victory to compensate for the loss of someone but it's better to have been able to have one to say goodbye to such an extraordinary player.”
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