An 8-2 win against Walsall sealed a superb season at Ashton Gate, with City also claiming the Johnstone's Paint Trophy at Wembley.
Speaking in the wake of a parade through Bristol with his players, Cotterill has said: "What my Nottingham Forest experience taught me was that I could handle a big club, the demands, the pressure, 100 percent.
"I didn't speak to anyone outside of family and friends for about two months after I was sacked by Forest because I was so shocked.
"I knew the job I was doing was a good one yet the public didn't because of how it was ended. I've got belief I can manage at the very top and I'd like to achieve that."
Another former Nottingham Forest manager, Alex McLeish, is poised to return to the British game after a spell in Belgium with KRC Genk which he feels has boosted his reputation.