Time is very important. IF for instance you had only your king and a rook, and he had everything still on the board but his flag fell. you would win. Do to time being part of the game. Yet because you didnt have enough items on the board to give mate at anytime later in the game it was a draw. I for one would have been happy with the draw in your game. Chalk it up to, you learn something new everyday.
I had a tourney game many many year ago(94) were I got first place in a quad do to this type of reason. I was behind in material, but his flag fell. I won the game and the quad. I admit toward the end I was moving faster to get his flag to fall. OF course back then they didnt have the increments, added to games. Which I am still up in the air if I like or not.
here's an easy way to put it. if you run out of time, the worst POSSIBLE result for you is used. Sometimes it's a draw, sometimes a loss.
There was once a problem in OTB chess when white had K+Q vs. K and white grabbed his queen and placed it on the mating square. At that same moment, black called a flag fall on white and asked the arbiter to declare the game drawn. should the game be drawn?