The 22-year-old attacker was listed as a substitute for Thursday's first-leg clash at Stamford Bridge but joined the group warming up at half-time after a poor first-half performance from the Blues.
Christopher Nkunku helped calm Chelsea fans' nerves by converting a penalty in the 50th minute before Enzo Fernandez set up Noni Madueke for the winner.
Palmer was one of three substitutions made after 58 minutes, replacing Marc Guiu, while Madueke and Fernandez were the other two players brought on.
The England international was spotted feeling his hamstring as he made his way off the pitch and straight down the tunnel.
Maresca suggests Palmer will be ready for the weekend
Concerns grew around the seriousness of Palmer's injury as he left the field, but Maresca provided a positive update on his star attacker, indicating that he will be fit for the upcoming trip to the Molineux Stadium at the weekend.
In his post-match conference, Maresca said: "Cole felt something, but he looks fine. They already checked him. He looks fine, he looks okay.
"So hopefully there is not any problem and he can be available for Sunday's game."
Palmer was Chelsea's standout performer in a fairly underwhelming 2023-24 Premier League season, which was his first in West London since transferring from Manchester City.
The 22-year-old England international scored 27 goals for the Blues last term and was awarded the PFA Young Player of the Year earlier this week following his exceptional campaign.
Maresca comments on his team's performance
While Chelsea secured the win they were aiming for on Thursday night, boos rang out around the ground from the home fans at half-time with the scoreline still at 0-0, and that continued at different points in the second half as well, even after the Blues took the lead.
When asked by a reporter if he had a message for the fans, Maresca responded, "The message is quite clear.
"At the moment we are learning how to manage the game. Probably in some moments, the right thing was to do exactly the same thing, but on the opposite side.
"So, for me, the intention to keep the ball is the correct one - especially when you are 2-0 up. The intention is good, but probably where is not good.
"So I can understand [fans booing], but overall I think it was important tonight the win game - clean sheet, we did nine changes, we had players like Renato [Veiga] excel, Pedro [Neto], even Marc [Guiu], it was Filip Jorgensen's first official game. So many good things."
Chelsea lost their opening Premier League match of the season 2-0 to Manchester City and will resume league action this weekend with a trip to face Wolverhampton Wanderers on Sunday afternoon.