Quinn had been a strong supporter of Bruce as manager and his departure raised doubts about the security of Bruce's job.
Bruce has been reassured by the new chairman that his position is safe, although the former Manchester United defender admits that Sunderland need some positive results.
"[Short] reassured me that everything's okay," said Bruce.
"I need a few results, it's as simple as that. Niall will still be in touch with the owner, I will still be in touch with the owner.
"Whether there will be patience, I don't know. That I can't answer you."
Sunderland take on Arsenal at the Emirates on Sunday afternoon.