When the 49-year-old took the helm at Ashton Gate in December, City sat 23rd in the league table, but five months on, Cotterill's side are now 12th with just one game left to play.
The former Nottingham Forest manager believes the positive attitudes and the help of everyone at the club have helped him turn things around.
"Making sure a club of this size does not end up in League Two has been quite stressful and, without the help of a lot of people, it would not have been possible," Cotterill told the Bristol Post.
"A second relegation would have been disastrous and there would have been cuts on the pitch, cuts off the pitch and a drop in the number of people watching us. There was no way we could allow that to happen.
"I've had help from the owner and the board right down to the tea lady. Without the continued support of the kit man, the analyst, the coach driver and everyone else involved, there is no way we would have been able to pull this off.
"This club is full of really good people and we have to try to make sure we build on that and everyone stays strong.
"It is easy to stay strong when you are winning, but a lot more difficult when things go wrong and you are trying to pull everything together.
"I wouldn't have been able to turn things around without the positivity that has surrounded this football club. That has come from the fans and the media as well as the staff, and I would like to place my thanks on record."