Forest were slow coming out of the blocks against the Robins, and found themselves 2-0 down within the opening 15 minutes of the match.
It proved to be a deficit that they were unable to overcome, and Prutton believes that their mind-set was poor going into the game.
"It's got to be a mentality thing - it's not tactical, it's not technical and it's not to do with ability," he said. "It's about how a team approaches that first 15 minutes. Players need to get pumped up to perform as soon as the whistle blows, and they're not doing that at the moment.
"Dougie Freedman knows he wants them to play, and he knows his tactics. He's set his team up, and they haven't performed for him. It's their mentality."
Forest's defeat to Bristol City has left questions being asked of their squad, as the Reds' form has been poor of late.
The Midlands outfit had a spell during early September where they appeared to be starting to click into gear, but they have failed to win any of their last four fixtures.
Although Freedman is having to deal with a number of injuries at the moment, the Reds' performances have still been well short of the standard required, and there is a realisation that they need to end their poor run of results quickly.
Forest are currently sat in 14th place in the Championship table, and their next fixtures comes against Burnley on Tuesday evening.