If all the flaky burnt stuff is gone, don't worry about a stain. The pan is still usable. Many of my stainless steel pots and pans have dark spots on the bottom (okay, I'm admitting that I've burnt stuff many times.
The last seriously burnt pot that I had, I soaked it in a bit of water (about 1/2 inch) with dawn, then let the water come to a boil on the stove-top. Let the water cool a bit, then scrub with an abrasive pad (sponge or scrub brush). Then I ran it through the dishwasher.
The inside bottom is smooth to the touch, but there is a dark stain.
Be very careful with what Toots suggested. It really depends on the type of material your handle on the pot is made of. Calphalon is high-quality cookware. If yours is like mine, a cheaper brand with a hard plastic type of handle, do not do this.