West Ham only signed Payet from Marseille in the summer transfer window, but his brilliant start at Upton Park has seen them offer the attacking midfielder improved terms already.
Payet has now committed his future to West Ham for the next five years, despite interest from China (Sky Sports), but Moyes feels that the fact Slaven Bilic had to offer his play-maker a new deal shows the power that players have these days.
“They bring him and he does well [and they have to offer him a new contract],” the former Manchester United boss said.
“If he played badly, he wouldn’t be taking less of a contract. But the minute they do well, they want a new contract.
'It’s very difficult for the clubs now, if a player comes in and does well, they come in and want more money.”
Payet has contributed six goals and four assists in his first 18 Premier League appearances, and his skill in possession has already made him a fans favourite at Upton Park.
And Moyes admits the the French international has unquestionably improved the Hammers’ play.
“He’s doing really well, and he’s given West Ham a real bit of swagger about them,” Moyes added.
Payet’s form has helped West Ham move into contention to claim a European spot.
Bilic’s men are currently in seventh place in the Premier League table, but they are hot on the heels of Southampton and Manchester United.