Actually you fail to mention which one of you ran out time. I suspect it was you as opponents last move is recorded == clear draw in that case. Obviously opponent did not have material
Finaly we get to the point. The OP ran out of time and as his opponent had only king (insufficient material) so the game is a draw under FIDE;USCF;chess.com; and any other rules you care to mention.
just to be clear for the benefit of the OP.
If a player runs out of time he loses the game UNLESS the opponent has insufficient mating material in which case the game is a draw. Do a search on here to what constitutes "insufficient material". A lone king is clearly such, but it gets complicated when other pieces are present and FIDE and USCF have slightly different rules.
Offering/claiming a draw... In normal play a draw may be offered and the opponent may accept or decline.
If however a "threefold repetition of position" has occured, or if 50 moves have been made with no pawn moves or pieces taken then any player is entitled to "claim" a draw. This is done by pressing the "offer draw" button, but in this instance the opponent is not given the chance to accept/decline the draw, the game WILL be drawn if the requirements have been met.
Other draws such as stalemate; or if a position arises so no player can deliver checkmate, will happen automatically
What was the final position?