The Dark Blues are sitting 13 points adrift at the foot of the Clydesdale Bank Premier League table with just seven games left between now and the end of the season.
But interim boss Brown is undefeated in four SPL games since taking over and came within several minutes of beating neighbours Dundee United on their last outing despite having Gary Irvine sent off in the opening quarter.
Brown was delighted with the fighting spirit they displayed that day and wants to see more of the same when his former Rangers team-mate Stuart McCall takes his second-placed side to Dens.
He said: "We can take a lot of hope and encouragement from the derby game. I was really pleased with the way we played for 70 minutes with just 10 men and didn't cave in. That spoke volumes for the character of the lads and we'll definitely have to be like that again for the Motherwell match.
"They have lots of talented players but it's our job not to let them play to their best. Our fans have an important part to play as well. They have been excellent in recent weeks and can be like our extra man. Hopefully we can give them something to shout about.
"We know it's a big ask to stay up with seven games remaining but we will give it our best shot. The boys are buzzing at the prospect of getting back into action and this game can't come quickly enough for them to show what they can do."
Motherwell scored four goals in their most recent 45 minutes of action, booking their top-six place in the process against Hibernian, but Brown is not urging caution.
Brown said: "We're going to be as positive as we can under the circumstances. It's going to be a very hard game but we need to get as many wins as possible in the games which are left and see where it takes us. Motherwell are a quality side but we'll focus on ourselves as always and what we are capable of.
"The lads know our own position and what we must try and do so there will be no shortage of effort from that point of view. We'll be as attack-minded as we can and hopefully that pays off for us."