Albion often looked the more dangerous side despite having striker Billy Kee sent off before the break - only for Freddy Eastwood to come off the bench and secure a 1-0 win for the Blues in the third minute of added time.
Brown said: "I think you've got to give Burton a lot of credit because their second-half performance was very resilient.
"They were very hard working and tough to break down and, in all truth, I couldn't tell you what formation we were playing at the end.
"But we threw all our eggs in one basket with the substitutions that we made and, strangely enough, one that was forced upon us through injury is probably why we ended up winning the game.
"We went to a back three and got some width, which we'd been lacking, and it finally caused Burton one or two problems.
"Before that we just didn't move the ball quick enough to break down the two banks of four.
"But I think the players deserve credit for being patient and all credit as well to Freddy for the goal.
"He always asks questions of the opposition and has a knack of getting himself on the scoresheet."