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The Radio 1 presenter claimed Roberts should be more appreciative of her wealth and success.
"Nicola is not the most striking one out of Girls Aloud, unless by striking, you mean ginger," said Moyles.
"It's nothing to do with her hair or the way her face or body is, it's that the sour-faced old cow never smiles - ever."
He continued: "She always looks peed off, like she doesn't want to be in the band. Someone should show her the Girls Aloud bank account because if she worked at Tesco's - and it would take a few years to build up to that level for her - she wouldn't be making the money she's making now."
Moyles added: "She's got a great life flying all over the world yet her face looks like she works at Netto."
Roberts responded to repeated criticism from the DJ earlier this year, commenting: "I can't stand him. It's no surprise I look miserable with him on my case.
"And he's such a good-looking bloke himself, isn't he?"
