Brown was unhappy with the 4-1 loss at Motherwell on Boxing Day, but believes his side can start to accumulate points to consolidate their top-six position entering the winter break.
The Dons' challenge at Dundee, who are nine points adrift at the foot of the table, is boosted by the availability of Stephen Hughes, Rob Milsom and Ryan Fraser following injury.
Brown said: "The lads have been left in no doubt that the result the other day was unacceptable. We must atone for that.
"We know that Dundee will be up for this game. They're running out of fixtures and other clubs above them are picking up points, so they have to get a response.
"After a good performance against the Old Firm they'll be fairly confident.
"We've got to make sure they don't get a result against Aberdeen. But my concern is not Dundee. My concern is keeping Aberdeen in contact with the top, because I genuinely feel with everyone fit we've a great chance of going on an unbeaten run.
"We're in a good position if we can get points over this holiday period."
Hughes is optimistic the Dons can climb the standings, with players returning from injury.
He said: "There's boys getting back fit. Hopefully we can get everybody back fit, competition will be high again and we can push on.
"We're still in a good position. We've dropped a few points, but I think that's maybe down to the squad and how depleted it is.
"We don't want to make excuses. We've got a couple of good games coming up which can push us right back up the table again."
Injuries created a particular void in midfield, but Hughes has been impressed with there performances of Scott Vernon in a deeper position.
"Scottie's done unbelievably," Hughes added. "I think he's played well in there.
"He's not complained once. He's a striker. He wants to score goals, but he's done a great job for the team.
"That's fair play to him. When you see how many midfielders have been injured it's unbelievable."
Hughes hopes Aberdeen can forget the Fir Park performance and show the form which produced victory over St Johnstone last weekend.
He added: "I thought that's the best we've played in a while. We looked sharp all over and we looked as if we were back to our old selves."
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