Why does one's rating go down after a draw, which is what happened to me when a game was drawn due to the three-move repetition rule?

Your rating went down because technically a player that you should have been able to beat is on equal standing with you. Your rating didn't go down much because it wasn't a loss. On that note, he didn't win, so his rating didn't raise by much either. This change in rating is just to reflect that both of your ratings should be closer together. There's a bit more to how it's calculated but I'm unfamiliar with the formulas.

Would this happen under the FIDE and ELO system?  Which ever, I don't agree that my rating should have gone down on the basis that it was a draw.

"Would this happen under the FIDE and ELO system?"

Yes,but depend on which rating system some tournament are playing.I heard that chess.com use Glicko-2 rating system.

You draw game with player who had about 150 rating points less than you.On every rating sytems you would lose some points.On some you would lose more on some other rating sytem you would lose less rating points.

Many thanks; yes I know chess.com uses the Glicko system, I was just enquiring as to whether this would happen under FIDE and or ELO rules as I wasn't sure.  Also, I've drawn a few games before on this site with players rated higher than myself, and their rating didn't allways go down and mine didn't go up either.