The German midfielder was supposed to lead the team in the penalty shoot-out loss against Frankfurt but decided to hand it over to defender Nico Schlotterbeck before the match.
"I gave Nico the armband because I felt I haven't been in the starting lineup much in recent weeks," said the 29-year-old to Kicker after the defeat.
"For us as a team, it's important to have some continuity and a permanent point of contact. He is doing the role really well right now."
Brandt scored the equaliser for the BVB in the second half of their cup exit against Frankfurt but could not help his side in the 4-2 penalty shoot-out loss, handing his team their second defeat in all competitions this season after losing Der Klassiker derby recently.
Schlotterbeck is expected to continue as Dortmund's skipper in the absence of the injured Emre Can.
Borussia Dortmund head coach Niko Kovac has extended his contract until 2029 after helping the Bundesliga club recover from a difficult start and re-establish themselves among Germany's leading teams.
Jonas Urbig is expected to start in goal for Bayern Munich against Viking FK in the Champions League on Tuesday after Manuel Neuer suffered a setback with a foot problem.
Viking FK defender Henrik Falchener has explained why he would prefer to face Harry Kane rather than Erling Haaland ahead of Tuesday's Champions League clash against Bayern Munich.
SC Freiburg maintained their unbeaten start to the Bundesliga season with a dramatic 2-1 victory over Schalke 04, scoring a late winner despite playing more than 25 minutes with 10 men.
