You're under no pressure to find the fastest, simplest, or most elaborate checkmate, nor are you under obligation to resign when you are down material. There are many ways to force draws-- and it's good practice for novices to play out checkmate without stalemating.
One time an opponent did the same thing to me. It was a blitz game and there was less than 30 seconds on the clock. I quickly advanced my passed pawn to promotion rather than trying to find a complex knight, rook, bishop combination that would not stalemate in the final seconds. My opponent called me another idiot who couldn't win without a queen and let the last of the clock run down.
If you checkmate with lone Q, he would have complained about you not promoting another one.