Antonio joined West Ham from Championship side Nottingham Forest in the summer of 2015, while attacking midfielder Payet moved to the Premier League outfit from Ligue 1 team Marseille.
"I can't even put into words how good this player is," Antonio told Sky Sports about Payet. "He's got all the attributes you need to be a Premier League player.
“He works hard and going forward he's got that special touch. He's just one of those players, he's magic.”
"You get better by studying and playing with better players," added the Englishman. "Each day in training he does something special. I watch him all the time to see what he does and hopefully he can make me a better player.”
Payet has been one of the best players in the Premier League this season and is leading the Hammers’ charge for a top-four finish.
The France international attacking midfielder has scored eight goals and created 79 chances in 22 Premier League appearances so this campaign.
The 28-year-old has a pass accuracy of 82% and a shot accuracy of 65%, and has won two headers, 55 dribbles and 13 tackles.
Meanwhile, Antonio has scored six goals and created 12 chances in 17 Premier League games this season.
The former Forest star has a pass accuracy of 65% and a shot accuracy of 42%, and has won 27 headers, 27 dribbles and 15 tackles.