Forest remain in the bottom three after a 1-1 draw at Barnsley on Saturday and Wales full-back Gunter insists they can ill-afford to slip up against the Robins on Saturday.
Billy Davies' side then face high-flying Sheffield United on Easter Monday and Tottenham youngster Gunter insists they must start picking up points to avoid an immediate return to League One.
"I desperately want the club to stay in this division," Gunter told
Forest's official website.
"We'd like to think being at home (against Bristol City) we can get three points. If the fans can stick with us, its a must-win game and I'm sure we can get a good result."