The England international has proved Chelsea's star signing since moving from Manchester City, who could not promise him he would play every week, for a reported transfer fee of around 40 million pounds ($50 million).
Palmer has scored 31 goals and provided 20 assists in 54 appearances across all competitions for Chelsea. This month he became their first player to win the England men's Player of the Year award since left back Ashley Cole in 2010.
"If we think that Cole is going to solve all our problems, it's a big mistake," Maresca told reporters ahead of Sunday's trip to Premier League leaders Liverpool. "We put all the pressure on his shoulders and that is wrong.
"Also because we have Cole but we have many players that are doing well. Noni (Madueke), Pedro (Neto), Nicolas (Jackson), Christopher (Nkunku), Enzo (Fernandez). It's not just about Cole, it's about all the squad."
Having finished sixth last campaign and 12th in the 2022-23 season, Chelsea hired Maresca in June after he guided Leicester City to the English Championship title in his first season in charge.
Chelsea are now fourth in the Premier League standings with 14 points from seven matches and trail Liverpool by four points. Their only league loss this season came against defending champions City.
But the Italian said his side were a work in progress.
"We work every day to be close to (Liverpool), knowing it requires us to work together day by day, time to approach and go close," Maresca added.
"The only way to try to be close is just to be focussed on the things we need to improve. To think where we can to be in four games, its a bit difficult. The only thing I can say is that we want to try to do our best Sunday."
"Game after game we are improving different things, but that game was a good game."
