City were left stunned at the Stadium of Light on Sunday as they suffered another 1-0 defeat, with Wearside proving to be an unhappy hunting ground for the Blues.
Sunderland scored with their only effort on target, but defended doggedly to claim a much-needed three points.
Success has offered them fresh hope in their efforts to steer clear of trouble, but Brown acknowledges that they need to start stringing results together if they are to climb the table.
He said in the Shields Gazette: "We all stayed together, stuck to the game plan and, at times, we could have scored again.
"We need to keep doing that after the international break.
"Winning any game is great, but Man City are a top side and they've got the best players.
"We matched them, especially in the first half, and then in the second half we had to work for it, and we did.
"Training will be good this week, we just need to keep this going and we're looking forward to the next few games now."
Sunday's appearance against City was Brown's first in the Premier League since January 2012, but he showed no signs of rustiness as he helped Sunderland to collect their first clean sheet of the season.
The former Manchester United defender added: "It was tiring towards the end, they put a lot of balls into the box, although the adrenaline helped me.
"Personally it was difficult, but as a team we were fantastic. I thought we played exceptionally well.
"As a defender, the clean sheet is the best thing about it. You don't concede any goals and you don't lose.
"That's our first clean sheet of the season and now we need to keep that going."