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The 18-year-old from Essex broke the tibia and fibula in his left leg after landing on a concrete floor while vaulting in November.
Less than a month before his injury, Bevan was part of the first British team to claim a World Championships medal, when they won silver in Glasgow.
"It hurt my head and heart knowing what I had done," he told BBC Look East.
"My coach tried to jump in front of me to stop me from seeing what had happened - but I had already seen it."
Bevan won a series of junior titles before he claimed bronze in the pommel horse at the 2015 European Games in Baku.
He had hoped to continue that progress at the Olympics in Brazil but, with only 247 days until the Games, he knows it will be a challenge to be ready in time.
"The most important thing for me is getting back to full fitness so I can carry on my gymnastics career," he said.
"I don't think the Olympic Games is fully out of reach, it is going to be tough, but there is still a small chance I can push for a place in that team."
Gymnast Brinn Bevan believes he still has a "small chance" of competing in the Olympic Games in Rio next summer.