Wales slumped to their biggest defeat in almost 16 years to leave their World Cup qualification hopes in ruins.
Chris Coleman, the manager, said: "I'm embarrassed about the result and I take responsibility.
"6-1 is an absolute hammering and it could have been more. That stings me even more. I did not see it coming. We were confident of getting something here, but we can't accept that level of performance
"Disappointment is an underestimate and it was men against boys. The goals we conceded were criminal and you can't gift goals like that at this level. There were far too many individual errors. Words fail me. You have to play with pride and we didn't do that. It was a dreadful performance."
Following their opening Group A loss to Belgium, Coleman's side now have a mountain to climb after just two matches. Aleksandar Kolarov, the Manchester City left-back, opened the scoring in the 16th minute, before providing the assist for Zoran Tosic's close-range strike eight minutes later.
Gareth Bale offered Wales a glimmer of hope with an excellent 30-yard free-kick. But Serbia, who had failed to score in eight of their last 10 internationals, exploited poor Welsh defending with Filip Djuricic, Dusan Tadic, Branislav Ivanovic and Miralem Sulejmani inflicting further punishment.