Jordan made the accusation after referee Rob Shoebridge gave a goal kick rather than a goal following Freddie Sears' first-half effort during Saturday's game between the two, despite the ball clearly bouncing back out of the net.
The Palace chief and his manager Neil Warnock have since blasted City, believing they should have either told the official it was a goal or allowed Palace to score straight away.
"For Crystal Palace to call us cheats is out of order," Lansdown told the Bristol Evening Post. "I understand Neil Warnock is upset but for his chairman to accuse us of cheating is discourteous and unnecessary and doesn't help his case.
"To cast us in a bad light is uncalled for. It is part of the game and he has I am sure been on the right end of such decisions. I have little time for him.
"The thing that's really annoying me is we're being labelled as cheats and a disgrace to football. We're not, we took a referee's decision and abided by it."