There are two interesting physiological markers for exertion that can be very helpful.
When you start hearing yourself breathe (likely what you call panting, but probably a bit earlier) you have passed about 60% Heart Rate.
This is useful, since you want to be running harder than 60%.
When you can no longer talk, you are closer to 85% which is needed for harder workouts, but on longer slow runs, you want to avoid.
So it is possible, if you are just getting started, and finding that breathing is consuming you, that it is a matter of taking it a bit easier, until you get your base fitness built and are more efficient.
It does take some time, and the best way to get there faster is just keep running.