No, you don’t. As a percentage maybe, but that’s irrelevant.
It is a much discussed topic. I feel like the best answer for you is more or less yeah. In my opinion it does not matter at lower levels. Some even think komi should be higher on 9x9 because you get influence on basically the whole board with the first move. You can search the forums if you want it has been discussed already. (here for example: Is a komi of 5.5 really appropriate on a 9x9 board?)
If you are interested in statistics you can look at database of proffessional 9x9 games here Waltheri's go pattern search - 9x9 games. Seems that black wins slightly more often.
Don’t worry about komi and/or one loss. I would be more concerned about the fact that you both kept playing totally unnecessary moves in your own territory and thus lowered your score. In Japanese rules ONLY the empty interesections count as points. You DO NOT have to completely surround opponent’s dead stones in your territory for them to be your prisoners. 