The Latics were beaten 2-1 by the League Two side on Monday night as they exited the competition in the first round.
"In the second half, we have to do much better. It was unacceptable," Rosler is quoted as saying by BBC Sport.
"You need more than three or four players out there having a normal game when you're in a cup game because you know the lower-league team will raise their game.
"If you are not going for 90 minutes you can get hurt - and we got hurt. Burton Albion did very well by sitting deep but we made too many mistakes. It was not good enough on the night."
Wigan continue their Championship campaign on Saturday when they travel to Charlton Athletic.