"We believed in ourselves and we put in a solid performance, and the double 16s that Ricardo threw were so important," said Schindler, the world number 18, praising his 28th-ranked partner.
"We are delighted to go through. German darts is in good shape right now and we will continue to push forward."
Former BDO world championship finalist Bobby George said the English duo had underperformed.
"When you play in pairs, it's a different sort of game - you're not used to the gap between throws," he said.
Three-time BDO world champion Glen Durrant told Sky: "The walk-on for England, you could barely hear yourself. It was intimidating, a partisan crowd, but surely the Lukes will learn lessons."
Schindler and Pietreczko will next meet Australia's Simon Whitlock and Damon Heta, the 2022 winners, after they defeated debutants Argentina 8-1.
Former World Championship finalist Whitlock said afterwards that England's defeat had not been a surprise to him.
Heta added: "They probably relied on each other, thinking 'Oh, he'll do the business'.
"But the conditions weren't great. The crowd was all for Germany so it was probably brutal out there for them, but they will take it as another learning curve and probably get stronger - unfortunately for the rest of us.
"Fair play to Germany, they played good darts, but we are just worried about us and what we have got to do."
The Netherlands, represented by Danny Noppert and Gian van Veen, advanced with an 8-0 whitewash of Scotland's Gary Anderson and Peter Wright, while Wales' two-time winners Gerwyn Price and Jonny Clayton were 8-2 victors over the Philippines.
Northern Ireland's Josh Rock and Daryl Gurney, the fourth seeds, defeated South Africa 8-2 to set up a last-eight tie against 2019 runners-up Republic of Ireland, who are represented by William O'Connor and Keane Barry.
Quarter-final draw
Germany v Australia
Northern Ireland v Republic of Ireland
Wales v Hong Kong
Netherlands v Czech Republic