Jay,
I have been doing brakes for over 40 years, and the old way of just pushing the pads back into the calipers has been the way it was done for many years, but is not the correct way to do it now.
If your brake pads were wearing very thin, your master cylinder can gulp in some air if the fluid gets too low. As explained earlier, moisture gets into your brake system from the atmosphere and your brake fluid willingly attracts moisture. That moisture turns to steam and that creates a spongy pedal. If you seals go bad, they can suck air into the system as well.
When was the last time you flushed the fluid?? If you have not bleed the brakes or flushed the fluid, you need to try that first. The fact that you assume that no air got into your brake system is a false asumption.
The spongy pedal is caused by air or mosture in your brake system. Flushing the brakes will resolve those problems. Just bleeding your brakes will likely imrove the pedal feel.
...Rich