Why is my heat shield failing?

Recently I did a Duna mission in Kerbal Space Program. I was landing my capsule on Kerbin (from Duna). I had a Heat Shield (0.625m), a Mk1 Cockpit, parachutes and a SAS. My periapsis was 19 kilometers. So everything was set.

When I entered the atmosphere at 2500 m/s everything was going fine until I started getting heat warnings and eventually everything exploded/burned up, including the heat shield. How do I prevent that?

The 0.625m heat shield is inappropriate for an 1.25m stack. The MK1 cockpit has a diameter of 1.25m.

There is no need to circularize around Kerbin first as other comments suggest. It is perfectly possible to re-enter from an interplanetary trajectory.

19km might be a bit deep, though. I usually aim at 25km for a return from the mun and would not aim deeper for an interplanetary return. I'd say 25-35km should be deep enough to capture but high enough to trouble with overheating, if you have the right heat shield.

Remember that you want to minimize two things: Peak heat flux, and total heat energy absorbed. Coming in too shallow will mean you don't capture (which isn't as bad in KSp as IRL due to unlimited life support), coming in a bit too shallow will mean you spend too much time breaking and absorb too much total heat, and coming in too steep means the peak heat flux is bigger then what your craft can tolerate.

From your description, it is not entirely clear whether or not you had a problem with total heat absorbed or peak heat flux, so react accordingly.

Further good reading is here:
How do you tell if re-entry will destroy your ship?