The Gelschenkirchen outfit were 4-0 adrift inside half an hour at the Allianz Arena, with Arjen Robben netting twice and David Alaba and Mario Mandzukic also getting their names on the scoresheet.
An own goal from Rafinha brought a second-half consolation for Schalke, but Robben deservedly grabbed his hat-trick and Bayern's fifth from the penalty spot in the 77th minute.
The embarrassing defeat came just three days after Schalke suffered a 6-1 home loss to Real Madrid in a UEFA Champion's League last 16 first leg tie.
And Keller was unable to hide his frustration, insisting that the team must apologise to supporters for the "extraordinarily bad" display.
Speaking to Sky Television, he said: "It was an appalling first half. It was catastrophic. It really was an extraordinarily bad performance.
"We fell apart. We conceded a deflected goal after two and a half minutes. You could see from then on we hadn't put Wednesday's defeat to Real behind us.
"We were frightened and did none of the things we'd said we would do. We owe our fans an apology. We had more courage in the second half. It's okay to lose here, but not like that."
Despite the crushing defeat, Schalke had previously gone seven league matches without a loss and Keller's men remain in the final Champions League spot.
