David Wagner's side won their Championship play-off final against Reading 4-3 on penalties after a 0-0 result and they will become the 49th different team to play in the Premier League in the 2017-18 season.
Palmer, who only made his professional debut this season after Chelsea agreed to loan their promising youngster to the Championship side, revealed that he was keen to stay at his loan club even if they didn't earn promotion at Wembley.
"Of course, I want to stay. To be part of it this season, I feel like I don’t want to leave it now," Palmer told Goal. "It is unfinished work. So hopefully we can enjoy the next few days and then the talks will begin ahead of the next season.
"I think if we would have stayed in the league [Championship] then I would have loved to have come back anyway. We have gone up so it is an even bigger incentive to come back so we will just see what happens over the next few weeks and take it from there.
"It is unbelievable for me because I was out for four months and I didn’t think I was going to play for the club again and to be involved and win at Wembley is unbelievable. I can’t describe my feeling at the minute.
"To be promoted to the Premier League in my first season at 20 years old... It is the best feeling ever. My best footballing moment by far. You can play Under-23s for years and win Youth Cups, that’s been unbelievable but from the first game in a professional environment where the fans have been really passionate.
"Everyone is playing well, it means the world to everyone, it is a completely different experience."
Palmer's loan spell has been successful and he scored on his debut after only one minute, with his second touch as a senior footballer. He has gone on to make 27 appearances for Town despite a long spell out with a hamstring injury.
Huddersfield prepare to face the likes of Palmer's parent club Chelsea next season and he went on to reveal how much he has enjoyed being part of the Terriers' success.
"I feel like everyone is [delighted to make the Premier League]," Palmer added. "The commotion in the dressing room was great. Some of the guys have been Championship players for years and to get promoted as the underdog has been the best feeling.
Professional Debut & my First Touch was the match winner!Moment I will never ever forgetNever Question GodsTiming pic.twitter.com/4mNEPSpEdu— Kasey (@kaseypalmer45) August 6, 2016
"Everyone wrote us off and to come out on top again and again just sums us up. No disrespect to the Reading fans but you can sees who’s fans [were the loudest] today. So it is just a pleasure to be a part of it, it has just been an unbelievable season and we have created history.
Chelsea had over 30 players on loan across Europe, with many playing in the Championship alongside Palmer, who credited their system with helping him develop for a career at the top of the game.
"To be fair, I think there’s a few [loanees who have been successful]," He continued. "Christian Atsu [at Newcastle], Fikayo Tomori [at Brighton] and me and Izzy. It has been a successful season for the Chelsea loan boys so it has been good for everyone really.
Kasey Palmer's play-off final medal. pic.twitter.com/gUN7aTF5SJ— Chris Wheatley (@ChrisWheatley_) May 29, 2017
"Because I got injured we didn’t really get to play together as much as we liked. It is great for Izzy, just as much as me to come on loan and get promotion at 20 years old. I can’t think of anything better."
Palmer will celebrate the club's achievements with an open top bus parade on Tuesday evening through Huddersfield.