The pair were due to address the media ahead of Friday's British light-heavyweight title bout, but the challenger was unable to attend due to alleged travel problems.
"It is total disrespect from Danny to the press, Sky Sports and to me - it's pathetic really," Bellew told Sky Sports News. "I know what he's trying to do and there's no point trying to play mind games with me.
"I don't eat Big Macs but I'll make an exception on Friday night - he's getting chewed up and spat out. The problem is that he's only coming for the cheque, he might walk off with a good payday but he'll have a big defeat and a bust up face to show for his night."
Bellew lost his unbeaten record to Welshman Nathan Cleverly last October when the pair went head to head for the WBO strap.
The Liverpudlian fighter has since hit out at the world champion for not granting him a rematch.