Esse left Millwall for Palace just last month.
Esse told Palace TV: “It was a big win today. It meant a lot for us, the boys, the staff, the manager. We're into the next round, the quarter-finals, and it's an achievement to be proud of.
“Obviously, personally, it's always good to come to your home and obviously play your old team, where I basically grew up and started playing football. It was good to see some familiar faces, but then when it comes down to business, there was only one team that was going to win – and that was us. I'm happy we've won and we're through to the next round.
“Personally, on my performance, I know I'm growing, I'm still learning, getting better game by game. I just want to show the fans more and more every time I touch the pitch. I know it will come, so I've just got to stay patient and obviously give my all.
“I'm enjoying life at Palace so far and now I've just got to keep going, keep working hard.
“I'm enjoying it. It's a different environment, the best league in the world, top players in the world. I'm looking at players in my position: Ebs (Eze), Ismaïla Sarr, who also played in the Championship. These are big players.
“It's not just about always wanting to play, which I always do, always wanting to start. But sometimes you've got to watch and take little tips from each player's game and add it to yours.
"I'm enjoying learning at the moment so far, and also can't wait to make more of an impact – but as I said, that comes with time, and obviously you've just got to stay patient.”
On his reception from his former Millwall fans, with some light-hearted boos heard, Esse also said: “I'm not fussed, I know what the fans are like!
“But yeah, at the end of the game, it was a nice touch for them to clap me and sing the song again, that I'm one of theirs.
“It was good, but obviously we won – and South London is ours.”