Harkins had a first-half goal disallowed before 10-man Dee lost 5-0 to the leaders to stay 15 points adrift.
Brown, who took interim control of the team at the weekend, knows his team have been lacking in the final third this season, but he feels there are ways of increasing their threat when they face St Johnstone at Dens Park on Wednesday night.
And playmaker Harkins, a January signing from Kilmarnock, is central to his hopes.
Brown said: "There is a fine balance between going gung-ho and throwing the game away; you have to be in the game.
"We have to defend well. You look the first goal and the confidence goes.
"But I will be encouraging players to get into the final third and create chances.
"We have a player in Gary Harkins. He is a gifted footballer, he has vision.
"If we have players to make the runs in behind, that is something we have probably lacked.
"You need someone with a wee bit about them; you saw that from Gary against Celtic.
"Bairdy (John Baird) will work the defences but I'd rather he did that in the parameters of the 18-yard box, not out in the wide areas.
"We need to get the wingers to work with the full-backs and get into areas where we can get balls into the box."
St Johnstone manager Steve Lomas is looking for his players to grit their teeth and get through a hectic period.
He said: "I think our schedule is the worst of all the clubs.
"The Hearts game when it comes will be the sixth match in 23 days, then we have three weeks off, which is a bit mad.
"It is a very tough schedule so there has not been a lot of training done, it is all about recovery between the games."