The 18 year-old reached his latest career milestone in the 3-0 win at Turf Moor after 12 years with the Club.
"I've been at the Club since the age of six and it's a proud moment for me and I'd just like to thank my family, friends and everyone who has helped me get to this point and their support," said Palmer.
"Sunday wasn't very good for us, but it's all about how we reacted and we played we today and got the job done.
"I'm just glad we are in the next round."
Regarding his first team debut, he added: "It was great, all the lads made me feel really welcome and I've been training with them for a while now.
"It is sad my family can't be here, but hopefully, when things are back to normal, they can come and see me play again."
And the teenager admits playing alongside Kevin De Bruyne for the first time was something he'd hoped would happen sooner rather than later.
"I've been watching him as I've been growing up and now to be training with him and playing with him this evening was fantastic - he's just phenomenal."
You can watch a full-match replay of every City men and women’s first team game within 24-hours of the final whistle on CITY+.