The North-East England outfit sit 19th in the Premier League table, some four points behind the safe West Brom.
Sunderland have a game in hand on West Brom, but their chances of survival are slimming by the fixture - they have lost their past three, and are winless in six.
Brown pointed the finger at his side's forwards, given midfielder Adam Johnson is the club's leading scorer in the league with eight this campaign.
"We just can't put our chances in the back of the net at the moment," Brown said.
"We're playing good football but it doesn't count if you're not getting the points. But you can't give up, all we can do is stick at it. We've just got to keep going and keeping battling on. If anything, we have to give even more."
Brown said support from Sunderland fans in the run-in was crucial, but understood a lack of results would see the paying customers lose faith as the club's attempt to secure a seventh consecutive term in the English top flight looks under threat.
"It helps when they're cheering and getting behind us like they did in the second half against West Ham, when we were pushing on," Brown said.
"But it's edgy times at the minute so you can understand the disappointment.
"When you've played well and lost it's still rubbish.
"You get in the changing room and it's the same feeling as any loss.
"All right, we've played well, but we all know that we need wins and we need points."
Among Sunderland's remaining fixtures include Tottenham, Manchester City, Chelsea and Manchester United (all away); and fifth-placed Everton.
