you should , without question, have gone for perpetual check. This is a draw. Obviously your opponent isn't in a better position, he has more material in a drawn position
Question of ethics...

it is perfectly fine ethical to draw in this position- it is part of winning to make sure your opponent has no perpetual check.
in this case your opponent should have calculated a way not to give you that possibility. therefore a draw is a correct outcome in this situation.

Check the meaning of "draw"...in chess game you can get draw by repetition or draw by by agreement or draw by inssuficient material....draw by repetition has to be claimed, draw by agreement is agreed by two players and is not a matter of just one side..when playing live chess here on this site, you claim draw by pressing the button...the repetition draw -as you call it, cannot just happen here , since the clock will tick, unless you press the draw button, and you can loose on time..you only need three times the repetition of the same position(NOT necessarily in the row) to claim the draw by repetition...just check the draw in rules of chess..good luck!!
Thank you all for the answers, you made me sure about this thing...
@ alanford, Well obviously this chess game on this site is able to recognise this kind of repetition draw, after chasing for about 8 moves in this perpetual chess, I (thinking of not being recognised after 3 moves) made a move with my rook to not chess position and sudenly then the game ended with draw and 0.5 point for everyone...

http://www.chess.com/forum/view/livechess/third-repetition-rule-not-draw-bug
Just check the above link and make sure you can claim draw by repetition after three times the same position..it could be that your opponent claimed the draw by repetition..and you pressed nothing.... and suddenly the game ended with draw by repetition.Be well..

Thank you all for the answers, you made me sure about this thing...
@ alanford, Well obviously this chess game on this site is able to recognise this kind of repetition draw, after chasing for about 8 moves in this perpetual chess, I (thinking of not being recognised after 3 moves) made a move with my rook to not chess position and sudenly then the game ended with draw and 0.5 point for everyone...
It's not automatic - you do need to claim it. If you didn't, your opponent must have done so.
Hi chess fans,
I have
a question about my yesterday´s game. The situation was like shown at the picture, I was white and I was to move. It is obvious, that I have a weaker position as regarding to the amount of figures, but on the other hand my rooks could still keep the King in chess position (only 2 places to move), so I offered draw, but my opponent declined it. So my question is, if this is considered as a draw situation, and I should have kept him in chess till the repetition draw game happens or on the other hand I (as a question of ethics) should have to play other moves and definetly later loose the game...Thanks for your answer...
Palobakala