Good comeback. I've made many such comebacks against 1700s and 1800s (daily here) after dropping a piece because of moving too fast.
Ratings here are pretty inflated though, and only start to compress slightly higher up the ratings. So it's very possible to defeat 1800s here with piece odds.
Although I have no clue why you played Kd1. It's like one of those moves where you're scared, and so want to end it by just giving the opponent everything he/she wants. Nd4 just sacrifices an exchange (while keeping your king safe), which is very little considering that black was threatening to win your queen at least.
I've seen too many bizarre (to me) posts where players either express disappointment that they "had" to resign because they dropped a piece - one in a case where a pawn was lost! - or they express anger that their "beaten" opponent kept playing after dropping a piece.
I, White, dropped a rook on move 13 to reach this position:
If I had nothing to attack with, I'd have resigned here, but I hoped I could launch an all-out, desperation attack, getting in moves like Ng5 and Qh5, and aiming every piece I could at Black's King while that h1-N that took my rook stayed at immobilied h1, his QR and maybe QB remained out of play, and his Q, B, and N clustered on the Q-side mostly stayed there while I attacked through the K-side gap in his defenses.
Here's how the game ended. my opponent resigning because I had a forced mate-in-2 (30...Rf7 31 Qe8+ Rf8 32 Qxf8#):
If you can form ANY plan that might gain a local material superiority and might work - even if it requires some poor moves by your opponent, do NOT give up if you're down in material and if you're up a piece, don't get lazy and think the game is won! Here's the whole thing for what it's worth. I'll post an annotated version at some point to explain why moves Stockfish considered blunders were the moves that won the game: