The president says the club rejected the sporting director's offer to quit and insists the youth system has done nothing but good for its young players
The Spanish giants are not permitted to sign players for the next two transfer periods for breaches relating to the international transfer and registration of players under the age of 18, although they have appealed the punishment.
Rumours were rampant this weekend that Zubizarreta had offered to resign if it made the situation easier for the club to deal with, but Bartomeu does not believe axing the Catalans former goalkeeper would have helped.
"Zubizarreta is a club man. The sporting director is doing a very good job, he helps us make our decisions," he told Catalunya Radio.
"On Wednesday, when the sanctions from Fifa arrived, we had a meeting with a group of club chiefs in the afternoon and it is true that Zubizarreta said that if it was a solution then he would walk.
"But his departure would not solve anything."
Bartomeu claimed now is not the right time to discuss what led to the sanctions from Fifa, but stressed that they will appeal to the world governing body that their method of integrating youngsters is a positive one.
"It is not the right time to talk publicly about why Fifa is criticising us, because the club is in the middle of the season. But we will, although I must say that in our youth football set-up there are many people involved that have done a great job.
"We will explain to Fifa that sport is something that integrates people and Barca do not only form the players as footballers but also as people.
"We now have a number of guys that can't play because of Fifa's criteria. And we have them here because their parents want them to stay here. They cannot compete but they can train."
"We have to let these guys play to integrate them into our society. Football is a sport of integration. And not only football, but also different sports where there is no problem for them to play even though their parents cannot be with them."