The former Southampton midfielder has been instrumental in Palace's recent resurgence, scoring four goals in his last three matches for the Eagles.
"Jason has been great for us since he came, he's a very talented player. It's good he's showing what he can do," Speroni told talkSPORT.
"The key for every player, not just for Jason, is to show that week-in week-out. He's been doing that for the last few weeks but he needs to move forward and manage to do that every single week. That's the difference with the top players.
"I think he can do that, so I'm pleased to see him doing so well."
Palace all but guaranteed their Premier League survival this week with a 3-2 victory against Everton.