Council staff said late yesterday no complaint alleging a breach of the code had been received.
However, councillors said none was justified as Cull had been provoked.
Councillor David Benson-Pope said Debenham's presentation had been "extraordinarily inappropriate" and it was "most unfortunate the mayor was put in the position he was".
"I don't condone the comment he made, but he did apologise for that."
Councillor Mike Lord also was "not that concerned" by the mayor's comments, adding he might have done the same.
"I believe the title of the mayor is worthy of respect," he said.
Councillor Rachel Elder said Cull appeared to have caught "a bit of foot-in-mouth disease", but clearly regretted his actions.
The council wanted public participation, and "grizzles" were part of the process, but respectful behaviour was needed on both sides.
Councillor Christine Garey said "extreme provocation" by Debenham put Cull in a "totally impossible position".
Cull was right to apologise, but "it's just not okay for members of the public to come into that situation and have a crack", Garey said.
Councillor Doug Hall agreed, saying Debenham was "totally out of order".