The Whites boss felt the result, clinched by Patrick Bamford's 90th minute winner, was a fair one.
Leeds had 75 per cent of the possession and mustered 21 shots, a dozen of which were on target. But Luton did have a spell in the game, when Leeds' grasp slipped.
James Collins cancelled out Bamford's first goal, Kiko Casilla was forced into a smart save by Harry Cornick and Matty Pearson put the ball in the visitors' net, only for an offside flag to curtail Luton's celebrations.
Bielsa's men regained control, kept plugging away and found a way to win in order to stay just two points behind leaders West Brom, who also picked up three points today against Sheffield Wednesday.
"In the first half it was a little bit easier for us, but in the second half we fought a little bit more," said Bielsa.
"As usual it is very difficult to win, if you don't fight, you don't have good condition to play. If you want to win, you have to fight, if not you cannot. I think that we fought and we could play as well.
"After we got the first goal we had a chance where we could have imposed a second one, after we scored the second goal we had two clear chances. But you've seen that the last ball of the match was for them, number three at the back post. When you have just a goal difference, deserving to win is not enough."
The compact pitch at Kenilworth Road presented a challenge for Leeds, along with a style of play employed by Luton to make the most of their ground's dimensions.
"I think that playing here in this stadium is not easy," said the Argentine.
"You play in a small space, there is always a difficulty for the team who attacks. When the pitch is small this difficulty increases. When you play in a small space the possibility to score when you are building the attack increases, that allows the team that is defending to counter attack. This is a team who are compact in defence, they recover and counter attack very fast and they play long balls after recovering. In this pitch long balls means box to box."
Bielsa was pleased for his centre forward Bamford who grabbed a 'deserved brace' that will further boost his confidence having broken a 10-game goalless streak last time out against Blackburn Rovers.
And he allowed himself a chuckle at the memory of centre-half Ben White storming up the pitch to play in Bamford for the opening goal.
That moment, the sight of a defender joining in the attack with such style and impact points the way forward for the sport, in Bielsa's eyes.
"You can say nothing about that, it's easy to value what he did. Everyone can realise it was a brilliant action. It's a way to describe where football is going. The attacker defends and the defenders have an involvement in the building of an attack. It is not normal that a centre-back gives these kind of passes," he said.
Luton were aggrieved that they were denied a free-kick outside the Leeds box in the moments before that opening goal, but play progressed so far and in such a way that Bielsa did not feel the goal was a direct result of that decision by referee John Brooks.
"We had 15 chances to score. I don't link the possible foul with the possibility of scoring after that. Probably you can interpret like that but the possible foul was 80 metres far from the opponent goal. In those 80 metres a lot of things happen. They are linked with the development and the finish of the chance. But I can understand the opponent and maybe the supporters linking it.
"I think the result was fair, a good performance from the team."