A 3-1 victory at home to West Bromwich Albion, combined with defeat for Everton at Manchester City say the Whites finish ninth in their first top-flight campaign since relegation in 2003-04.
It was a brilliant achievement but they developed considerably as the season went on from the joyous gung-ho football it began with to the greater defensive discipline after Christmas.
"It's difficult to offer a conclusion because on one side I'm very satisfied with what the team achieved but on the other side I feel like we could have added a few more points," he commented.
"If we divided the competition in two, in the second part of the season we conceded 50 per cent fewer goals than in the first part. Had we had that security defensively throughout the whole campaign we could have added those points I would have liked this season.
"But I'm satisfied with what we achieved. It is very difficult to win games in the Premier League very difficult, and on the other side I felt like we could have had a few more points."
Summer signing Diego Llorente made a big difference once he was finally able to start games in February, but the improvement started at Christmas, after the 6-2 defeat at Manchester United.
At that point the Whites had conceded 30 goals in their first 14 Premier League games. It was 24 in as many matches afterwards.
The only downside of the game, Pablo Hernandez and Gaetano Berardi's last for the club, was a late shoulder injury to Kalvin Phillips, who dislocated the joint in the first half of the season.
A fit Phillips seems certain to be in England's European Championships squad on Tuesday.
Bielsa, though, is optimistic he will be fit.
"Sincerely I haven't received any information about the gravity of it," he said.
"We all hope it's something that can be resolved quickly.
"Knowing the fortitude of Kalvin I know he has the resources to recover quickly."
As is the norm at the end of every season, Leeds must now wait to see if Bielsa will sign a new contract. He is stubbornly refusing to show his hand, but it seems very unlikely he will walk away.
"I can't imagine I will ever receive more than I have from Leeds and everything Leeds offers to a manager exceeds the expectations of those who have this job," he said.
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