The Chelsea midfielder, 23, was one of several high-profile omissions from the 26-man Three Lions squad bidding to end 60 years of hurt in North America this summer.
Despite scoring in the final of Euro 2024, Palmer missed out after an injury-hit and underwhelming Premier League campaign.
Tuchel also accused the attacking midfielder of failing to impact games when selected for his country.
With England preparing for their quarter-final against Mexico, Palmer has now spoken about the disappointment of watching the tournament from afar.
He admitted he "wishes" he was with the squad at their Kansas City base.
"Every player that plays football wants to be at the World Cup," Palmer told The Times.
"But it's a decision that I cannot change and a hard one, for whatever reason. But I'm just trying to enjoy the summer off - the first summer I've ever had off."
The former Manchester City midfielder has been spotted enjoying the off-season on trips abroad, including a visit to Wayne Lineker's O Beach in Ibiza.
Tuchel instead opted to include Marcus Rashford, Anthony Gordon, Noni Madueke and Bukayo Saka, a quartet with pace and power in abundance.
Palmer, a tricky, technical forward, believes he could have offered the Three Lions a different dimension.
Asked whether he had heard the support from fans, Palmer said: "Yeah, of course, it's nice, but I'm not there. I know what I could have offered - something different to what the manager has picked. But like I said before, I can't change the decision and I wish everyone the best."
"It's like anything. If you're told you're essentially not good enough then you're going to want to prove people wrong," he added.
Palmer's comments suggest the snub has left him with fresh motivation heading into next season at Stamford Bridge.