The defender made his first return to Selhurst Park on Saturday as Southampton recorded a 1-0 win, but Clyne was suitably impressed with Palace's display.
Jay Rodriguez secured the three points with the only goal of the game but Palace threatened to take a point through Yannick Bolasie and Mile Jedinak.
Southampton's win made them only the third team to beat Palace at home since Tony Pulis took over in November, and Clyne believes their form in front of their own fans will be the key factor in their survival.
"I would love to see my old club stay up," he said. "It is nice to see them playing in the Premier League where the fans deserve it.
"I think they've got a great chance in staying up, especially with them at home.
"They're getting points at home and they will be vital for them.
"If they get the wins at home, they can definitely stay up."
After four years at Palace, Clyne moved to Southampton in 2012 and has made 60 appearances for the south-coast club in all competitions.
