Did the other car stop at the light?

If the other car stopped at the light, it is most likely your
fault because it is very unlikely the car started moving before the
light changing to green. On the other hand, what is your car's
exact position when the light changing from yellow to red?
Most people in your situation would misjudge the timing of the
light change.

If you don't have a very credible witness, you will lose for the
simple logic reason above.