Vasdef,
You will get better results if you use individual resistors. That is, each LED has its own resistor and it is the LED/resistor pairs that are connected in parallel. Remember to calculate the individual resistor values based on the current of a single LED - 13.3 ohms times 9 equals 119.1 so use a standard value of 118 or 121 ohms. I am assuming you chose a current around 20mA and a nominal LED Vf of 3.5V so you are dropping 2.5V (at 6.0V) across each resister. 9 1/8W resistors will do the trick. The current will be around 25mA with fresh batteries (6.6V).
The reason for using separate resistor/LED pairs is that the Vf of your LEDs cannot be depended on to be real close. Therefore, connecting all the LEDs in parallel and using a single resistor will not result in the good current sharing - some LEDs will be much brighter - and pulling a lot more current - than other LEDs. A parallel array and single resistor only works well if you match the Vf in your LEDs.
Of course, there are lots of assumptions and limitations not mentioned. But this should get you up and running.
Henry.