The Dolly Blues have suffered just one defeat from their opening nine league games after winning the First Division North title last season.
With progress to the third round of qualifying in the FA Cup also safely negotiated, City are certainly beginning to make people sit up and take notice.
However, while Brown has been thrilled by the way his team have adapted to the higher level, he is refusing to get carried away. “We’ve played nine games – 11 if you include the two FA Cup games,” said Brown.
“It’s been a really pleasing start, but there’s a long way to go. There are 46 games – four more than last year.
“We have put ourselves on a pedestal as the league champions of the First Division North, but we are another team coming into the Premier Division.
“We have just got to do the best we possibly can and try to stay in the top half of the table and get as high as we can.
“We’re sitting in ninth with a couple of games in hand. We are in and around it and I’m certainly not looking to fall away.
“Without making any promises, we are just looking to do our best.”
City were comprehensive 4-0 winners over Droylsden in the FA Cup at the weekend and they followed that up with a resounding 4-1 victory over Whitby Town in the league on Tuesday night – both games at Giant Axe.
The two big wins were particularly pleasing for the boss as the team is beginning to find its form in front of goal, while staying strong at the back.
“To progress to the next round of the FA Cup was very pleasing with the financial rewards which are on offer and it also keeps the dream alive, as they say,” said Brown.
“We then backed that up with a resounding win over Whitby. I am pleased because we are improving our attacking play while still maintaining our defensive resilience.
“I think that’s 12 goals in our last five games and we’ve only conceded three.”
This weekend, City face a tough trip to fourth-placed Stourbridge, but Brown said: “We have held our own playinga few of the teams above us. We have beaten Shaw Lane and drawn with Warrington and Farsley.
Ricky Mercer (groin) and Louis Mayer (hip) are unavailable.