You don't need to resign because some one tells you, plus he maybe just raged for blundering such a winning endgame. So no, don't resign when a player not good at the game tells you so he wins 
Should I Have Resigned
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Dec 12, 2020
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#22
Waygorn wrote:
nklristic wrote:
The fact that he didn't know how to checkmate you confirms that you were right not to resign.
This is essentially what I tried to tell him, but he had said it was an easy win for him so I should've resigned, but I told him that the fact that he wasn't able to mate was why I played it out. He then complained that it only stalemated because we were low on time (I had about 10s and he had about 0.5s at the time of stalemate) and that I was being a d*ck for trying to run out the clock, which wasn't my intention.
That's your friend's fault for having poor time management skills.
Part of being a strong chess player is finding a balance between making good moves vs watching your clock. If he failed to checkmate you before his time ran out, then he doesn't deserve the win.
You were right not to resign.
There's a book titled "The Complete Chess Swindler," and this game fits a classic pattern. Your opponent expected you to resign, you didn't. He probably became frustrated, both because of your refusal and his inability to easily checkmate you. Eventually he made a fatal mistake. If I were him, I would be chastising myself for my inability to checkmate you.
As far as should you have resigned. If I had been your opponent, I would have been surprised that you didn't. But, what the heck, playing to checkmate is no big deal.