Answer: You don’t give me much information such as year and model, or disc/drum brakes. There are many things that can cause the problem you describe, but it would seem from your question that things were fine before the pads were replaced, so based on that premise I’m going to suggest that you check two things. First, were the brakes bled properly? On most classic cars, the pressure in the brake system is what pushes the brake pedal back up. If the brakes were not bled properly, it is possible that the pedal would not return all the way.
Second, since the rear brakes are almost certainly of the drum type, were the rear brakes adjusted properly after installation of the new pads? There is a “starwheel” which is accessed through a cutout in the backing plate for the brakes. This starwheel must be properly adjusted, or it could cause the symptom you are describing.
Many cars have a switch that shuts off the brake lights when the brake pedal returns all the way to the upright position. You don’t mention anything about the brake lights staying on, so I’m wondering if perhaps the brake pedal is in fact returning to the correct position? Perhaps the brake pedal just has a different feel than it did before the brake pads were replaced.