Carr said that he was disappointed to see the 'Give Me All Your Luvin'' singer guest on The Graham Norton Show last month, but accepted that the rival programme was probably more to her liking.
"I love Madonna so it felt like she was two-timing me by going on Graham Norton's show," he told The Sun.
"I'd love to have her on but I think I have made too many jokes about her dog-chew arms. See, that's why I don't get Madonna."
Carr previously defended Adele following Chanel boss Karl Lagerfeld's comment that she was "a little too fat".
"Lagerfeld is a vile old queen," he was quoted as saying. "If I see him I'd rip his grey hair off the top of his prune face. He needs to sort his face out. I mean, he could drop kick his jowls they're so saggy."
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Watch Alan Carr and other comedians chat to Digital Spy about the 'funniest thing on the planet' below: