I know this says mothers with depression, but I wanted to provide my input as a person raised by a single father with depression. He raised 3 kids by himself, a large chunk of that time on a disability income. We never went hungry or homeless, and I could not ask for a better parent.
There were times when he struggled, for sure. Our house was often quite the mess, dishes left in the sink, etc. But we understood, and we were still happy with what we had.
You may feel incompetent compared to other parents, but I can tell you that your children will likely be grateful for everything you did for them, as I am grateful for what my dad did for us.

Nobody is the "perfect" parent. Just do the best you can, that's all you can ask of yourself.