Allegri was axed just days after leading Juve to victory in the Coppa Italia final.
Bremer told Marca: "No one could have expected it, not even the coach, that it could end like this.
"It's not up to us players to judge, but I only have words of gratitude for the coach, He wanted me and made me grow."
Former Bologna coach Thiago Motta is expected to soon be confirmed new Juve coach.
Bremer continued: "I think he can improve a lot in everything. Allegri was an excellent defensive coach and, on the other hand, I think the next coach will really like possession. It will be a new challenge.
"Will the next Juve manager be Brazilian? Everyone is talking about it, but I don't know anything about it yet. We'll see who comes. We're Juventus, so it will definitely be a good manager we need him to continue to grow.
"In 2/3 years we will be fighting for the championship. We have a lot of young players and we need more experienced players. I think the club will get important reinforcements, also thanks to the qualification for the Champions League, and this will help us."