The Dolly Blues defeated promotion hopefuls Grantham Town 3-1 in what was a fine all-round performance at Giant Axe.
It was only their seventh win since the end of December in what has been a tough spell for City, who were promoted to the NPL Premier Division as champions last season.
While acknowledging the difficult past few months, Brow revealed he has not panicked.
He believes his team’s performances have been generally good, but they benefited from having more of an edge in their play against Grantham.
The seeds of Tuesday night’s win were sown last week during a team meeting, which led to a spirited display at home to runaway leaders Altrincham on Saturday.
Although that match ended in a 2-1 defeat for City, Brown admits he has been encouraged by what he has seen over the past week.
“Our performance on Tuesday night was the best we have produced in a while,” said Brown. “But it was a performance which we knew was in there. That’s why we have not been panicking.
“Even though results have not been brilliant, we always knew that we could put that kind of performance together.
This weekend, City have another tough proposition when they travel to Shaw Lane, who are fighting for a play-off place.
“We were the first team to beat Shaw Lane earlier this season,” said Brown. “They knocked us out of the FA Cup, albeit in a very tight game, so we know what they are about.”
City have a doubt over PNE loan striker Connor Simpson, who has a tight hamstring.