The SPL basement boys were a distant second-best in a one-sided contest at Dens Park, with Dundee's defensive frailties particularly evident.
The result leaves Dundee 13 points adrift of safety at the bottom of the table, but Brown promised his side would not give up fighting to retain their top-flight status.
"We didn't help ourselves with the goals we lost," said Brown afterwards.
"It's a steep learning curve. We have to do better in defence and that's the first time we've been guilty of that since I took over.
"But we'll keep battling on and won't give up on anything."