Pochettino's expensive squad have struggled for consistency this season, with some fans turning on the manager and the club's US owners after a 2-2 draw at Brentford in their previous game.
However, Palmer helped put a smile on the faces of the Stamford Bridge faithful by setting up one goal and scoring another in their 3-2 win over Newcastle United in the Premier League on Monday.
"There is so much talent at Chelsea," Palmer told the club's website. "The way that the manager works with us on the pitch, and the things he does with us, it's only going to get better.
"I'm sure if not next season, the season after, it's a project, everyone is young and everyone is trying to play well so you will see it sooner or later.
"We're still in the FA Cup, hopefully we'll win on Sunday (against Leicester City). We'll take each league game as it comes, hopefully climb the table and you'll never know where we finish."
Chelsea are 11th in the league on 39 points, three points behind Brighton in eighth spot having played a game fewer.
