The Dark Blues host the Buddies at Dens Park on Wednesday night as they attempt to recover from Sunday's Scottish Cup defeat by city rivals Dundee United.
Brown's side are bottom of the table by 15 points and many have written them off for the drop back down to the First Division come the end of the season.
But Brown is relishing the chance to pick up his first league win as interim manager and a fighting effort from Dundee to stay up.
He said: "It's another game for the players to look forward to.
"It's always disappointing losing to your biggest rivals in any derby game but we have to move on.
"It's good we have this opportunity to bounce back so soon and hopefully we do our best to take it.
"It promises to be a difficult game but we'll attempt to get the three points as we will do in every game between now and the end of the season."
Brown was happy with his side's battling qualities in last midweek's 1-1 draw with St Johnstone.
The 10-man hosts showed they are up for the fight and Brown hopes to see more such spirit when St Mirren visit Tayside.
He said: "We played well against St Johnstone and there are many positives to take from that.
"To be fair, everyone is pulling in the same direction.
"When you lose a player it's never easy but the lads here showed they have the fight to cope with that.
"We'll need that again as St Mirren are always hard opponents and they'll come here looking for a positive result."
Brown is urging the Dundee fans to keep backing their favourites after they watched them lose narrowly in the cup tie with United.
He said: "I think the fans appreciated what the guys put in as far as effort goes.
"They all gave everything and when they do that I'll never criticise them.
"We need the supporters to keep right behind us and hopefully they do that.
"We have to be attack-minded without going gung-ho.
"We know wins are ideally what we need to try to make up some ground on the teams above us.
"That's our job, to close that gap, and nobody here will ever be giving up on that."
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