Last season's runners-up reached this year's quarter-finals after a 2-1 home loss against the Russians on Wednesday gave Dortmund a 5-4 aggregate victory but the lacklustre performance received a muted response in the often noisy stadium.
"I really do not like this. Every time we lost possession you could hear moans in the crowd," midfielder Kevin Grosskreutz told reporters.
"We do not need moans, we need support. Afterwards you can whistle but during the game we need the support."
Injuries to key players throughout the season have been a constant thorn in the side of Juergen Klopp's squad and as the coach struggles to stick to a settled lineup, negativity from the stands has done little to help team morale.
"Some in the team are really affected by this," captain Sebastian Kehl said. "A home game should be a positive experience and not feel as if we have committed some sort of crime."
Home fans are likely to expect an even more cautious approach by their team in the last eight with European heavyweights such as Bayern Munich, Real Madrid and Barcelona lying in wait as Dortmund's injury list grows.
Defender Marcel Schmelzer could be out for some time after picking up a suspected adductor muscle injury and leading striker Robert Lewandowski is suspended for the first leg after being booked on Wednesday.
"We as Borussia Dortmund have to learn that a great success sometimes is hidden in a 2-1 defeat," said Klopp, who said he understood why players felt disappointed by the lack of atmosphere and support.
"In the last eight, there is the cream of European football and us. This team has really deserved this because of how they have fought on despite all the setbacks."
With central defender Neven Subotic and midfielders Sven Bender, Ilkay Guendogan and Jakub Blaszczykowski also missing through injury, Klopp will again need to shuffle his pack in the next round.
"Look at what kind of injury setbacks we have had to deal with and play football this season," midfielder Nuri Sahin said. "We are in the last eight and that is something that should be looked at carefully and honoured."
- Sports & Recreation
- Borussia Dortmund