Jurgen Klopp's men let the lead slip in Saturday's Der Klassiker with Bayern Munich as former Dortmund star Robert Lewandowski and a penalty from Arjen Robben cancelled out Marco Reus' first-half opener in a 2-1 win for Pep Guardiola's side.
Dortmund's setback at the Allianz Arena was their seventh league defeat of the season and their fifth in succession in the Bundesliga.
That poor return has left them occupying the relegation play-off spot in Germany's top flight and full-back Piszczek is aware the club must start picking up points fast to rescue their campaign.
"We need to realise that we need points now," he said. "We're down at the bottom and we need to get out of there as quickly as possible.
"That won't be easy. We need to work to make it happen and to try to pick up points."
Centre-back Neven Subotic believes Dortmund paid the price for failing to take their opportunities to build on the Reus' opener.
"We knew Bayern would start the second half aggressively as obviously they weren't keen on losing at home," he said.
"We were prepared for that. We tried to keep things tight at the back and to create a few chances at the other end.
"We did that to a certain extent - we had one or two opportunities to score again. The defeat hurts, especially after we went 1-0 up."
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