The Gelsenkirchen outfit were taught a harsh lesson at the Veltins-Arena as Jose Mourinho's side totally outclassed them to secure top spot in Group G.
With Sporting Lisbon beating Maribor, Schalke must win in Slovenia and hope the Portuguese club lose to Chelsea at Stamford Bridge next month in order to progress to the last 16.
John Terry headed the Premier League leaders in front after only two minutes and Roberto Di Matteo's side failed to respond, as they were put to the sword in front of their own fans.
Schalke's defending left a lot to be desired and Heldt pulled no punches with his verdict of their display.
He told the club's official website: "In the first half above all we did everything wrong that it's possible to do wrong,
"Even before going 1-0 behind we allowed them a chance and Ralf Fahrmann saved us at the expense of a corner.
"We put in an embarrassing performance, never went into challenges and didn't defend ourselves.Therefore we were deservedly thrashed.
"You can lose against Chelsea - they are ultimately a very good team - but the way we lost is not acceptable."
