Palmer came on as an extra-time substitute in Huddersfield's Championship Play-Off final against Reading at Wembley, which Wagner's men won 4-3 on penalties following a goalless draw in normal time.
And Palmer, who has spent the season on loan at Huddersfield alongside fellow Chelsea teammate Isiah Brown, wants to remain at the west Yorkshire club for the 2017-18 campaign after describing winning promotion as "the best feeling ever".
"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 [with injury] 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."
Chelsea currently have 35 players out on loan, and Palmer added: "I think there’s a few [loanees who have been successful].
"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."