The game was very different to the last Premier League meeting between the sides, when the Red Devils came out on top 6-2.
With very little experience of England's top-flight, the Whites have been learning as they have gone along, and five points and only two goals conceded in consecutive games against Manchester City (beaten 2-1), Liverpool (a 1-1 draw) and Ole Gunnar Solskjaer's side show the improvement they have made.
“We have constructed a solid group,” said Bielsa, whose goalkeeper Illan Meslier was only required to make one save of note, from a Marcus Rashford free-kick.
“Throughout this time they have made errors and learnt how to correct them. In the same way they've learnt to avoid avoidable errors.
“I have the feeling there's been a growth in the maturity and the experience to manage these games.
“The way to deal with difficult periods in the game has been improving. The capacity for the players to go up against these very good players has also increased – progressively but not in the definitive manner we can impose ourselves over the defence and avoid being overcome by attackers of the highest level.
“The team made a massive effort and this effort allowed the game not to become unbalanced for us.
“The game was played more naturally for them but even if they predominantly dominated, the chances on goal were similar, even if they did have more of the ball to attack and a lot more attacks than we did.
“I think a draw was sufficient reward given how the game went.”
Bielsa is not one to rest on his laurels, admitting that despite being unbeaten at home to the “Big Six” clubs they have faced in this season's Premier League – Tottenham Hotspur come to West Yorkshire on May 8 – there are improvements still to be made.
“In none of the games against these six sides except the one against Arsenal were we able to dominate to win the game,” he pointed out. “But the draws against Manchester City, Liverpool and Chelsea are good games to judge the players.
“Clearly at this moment we can't go into these games to dominate to go and win. At this moment we haven't managed to achieve that, apart from against Arsenal.
“I'm referring to the first half of that game as in the second half we had an extra player (with Nicolas Pepe sent off after 51 minutes).”
Asked if he thought his players could take the next step, Bielsa replied: “I can't affirm this. These things we have to demonstrate more than describe them but it is clear there is a margin for improvement.
“At the same time as a group it functions in a very united manner. They have created a base where they can go into every game with a fair optimism.”
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