Use an immersion blender directly in the pot, or transfer to a regular blender in small batches. Be careful with hot liquid—it can blow the lid right off the blender.
If you want it extra smooth, pass the blended sauce through a large sieve. The trick is to use the back of a large ladle and rub it against the bottom of the sieve in circular motions. This moves the sauce through quickly—most people try stirring with a spoon and get frustrated.
That said, a food mill is worth owning. They're cheap and last forever.
If you really have time, you can remove the skins from the chickpeas. Put them in a bowl of water, lightly rub them between your hands, and when you mix the water with one hand, use a small sieve to collect the skins from the top of the water. They float more slowly than the chickpeas, so you have a second to catch them.
A small but taller mixing bowl is key here if you have one, along with a small sieve.