The Radio 2 breakfast host, who took over from Terry Wogan earlier this year, told Richard Bacon that Moyles had “lost perspective” following his 20 minute rant over not being paid by the BBC for two months.
During his on-air tirade last month Moyles told his six million listeners: “I can’t tell you how furious I am. I haven’t been paid since the end of July and no one cares about it. No one’s bothered.”
The outburst led to wide condemnation with viewers venting their anger at the loudmouth DJ on Twitter and other social networks.
Former Radio 1 star Evans slammed Moyles’ approach, saying: “Why do you think you have the right to hijack a BBC microphone to make that complaint?
“Chris has got to go somewhere else.”
He also said the 36-year-old, who is the station’s longest ever serving breakfast host having done the job since 2004, is “way out of the demographic” of Radio 1’s target audience which is 16-29 year olds.
But Evans – who was beaten by Moyles in a recent ‘secret crush poll’ – had some good news for his rival.
The 44-year-old added: “I think he’ll go to commercial radio, he’ll get a massive pay packet, and I think he’ll do very well.”