The administration-hit club enter the second half of the season one point worse off than the 15-point deficit that they started the campaign with.
A late defeat against Edinburgh rivals Hibernian proved hard to stomach on Thursday night after Liam Craig struck a late winner from a disputed penalty.
The goal is among a number of late blows and controversial spot-kicks to have hit the team and Brown has called for some leeway as his squad battles on amid a transfer embargo.
But Brown insists no-one at Tynecastle will become disheartened by the succession of setbacks.
"We have got a will at this club and a way about us," he said. "We are a big, big club and everyone knows that.
"We have taken everything on the chin and come back fighting and we will continue to do that.
"There are not many teams that could keep fighting the way Hearts are fighting at the moment.
"I think the players deserve every credit. They are up against it every week and most weeks we have given a good account of ourselves.
"Heart and spirit is something that is not lacking here. There have been one or two games where we have let ourselves down but, on the whole, the effort the players are putting into games is magnificent."
With the gap at the bottom increasing in recent weeks, a home game against one of their nearest rivals is not something Hearts can afford to lose.
Brown said: "Every game we have had we have had to win it. It's a different game all together on Sunday.
"I was at Parkhead on New Year's Day to see Partick Thistle play against Celtic. Partick were very, very unfortunate to lose that game.
"They played very well, so it's a different type of game all together. It's another hard game.
"Our record at Tynecastle lately hasn't been what we wanted it to be. It's a game that we have got to look to win."