The Bundesliga side had not lost at Veltins-Arena this season, but put in a hapless display on Tuesday that severely dented their hopes of qualifying from Group G.
John Terry put the visitors in front after two minutes and Willian also netted before Jan Kirchhoff summed up a miserable first half by heading into his own net.
Chelsea eased off after the break but still added two more goals through substitutes Didier Drogba and Ramires as the home fans flooded out of the stadium early.
"It's hard to find words for this," said defender Howedes. "I can only apologise for our performance.
"We gave Chelsea too much space to play. They are so good individually and we let them score too many goals."
Schalke were unlucky not to equalise when just 1-0 down as a deflected Maxim Choupo-Moting shot looped over Thibaut Courtois, only to bounce back off the crossbar.
But overall they were simply outclassed by a Chelsea side playing with huge confidence and self-belief.
"After we fell behind so early we did not react well," added defender Dennis Aogo. "Apart from Choupo-Moting’s opportunity we didn't create any chances.
"I have to say that there was a big difference between the two teams."
With Sporting Lisbon beating Maribor, Schalke must now claim victory in Slovenia and hope the Portuguese outfit lose to Chelsea at Stamford Bridge.