The 28-year-old was booked in West Ham's 2-0 defeat by Watford last weekend and attracted criticism for making contact with opponents with his arms while jumping for the ball.
"I think it's becoming ridiculous," Moyes, who replaced the sacked Slaven Bilic earlier this month, told reporters. "I actually think as soon as the ball goes up everybody is already saying it's a foul against Andy.
"I'm telling you, you can only jump with your arms for leverage ... If we are now saying you can't use your arms for leverage then that isn't in the rules of football.
"Every time Andy plays, is everyone going to say, 'That's a foul?' If they do then we've got to say now that if you're six foot four you'd better go to basketball and stop being a centre-forward."
Carroll has yet to score this season for West Ham, who are 18th in the league and host Leicester City later on Friday.
(Reporting by Aditi Prakash in Bengaluru; Editing by Peter Rutherford)
