The other answer is correct, but I'll add some relevant code citations. Legally speaking, your stay in the United States is not limited.
First, you entered with ESTA. This means that you were nominally admitted under the terms of the visa waiver program, 8 USC 1187. This provides for a waiver of the requirement of 8 USC 1182(a)(7)(B)(i)(II). That is the requirement that a nonimmigrant be in possession of a nonimmigrant visa.
But what is a nonimmigrant? That is defined at 8 USC 1101(a)(15):
(15) The term “immigrant” means every alien except an alien who is within one of the following classes of nonimmigrant aliens—
Before we proceed to look at the actual classifications, we should look at the definition of alien. That is found at 8 USC 1101(a)(3):
(3) The term “alien” means any person not a citizen or national of the United States.
But you are a citizen of the United States, so you are not an alien, and none of this applies to you. Your stay in the United States was never limited, and all you have to do to prove it is to prove that you are a US citizen. You can do that with a US passport, or, as noted by Mast, with any other evidence of citizenship.
I would add that your entering the US without a valid US passport did violate 8 USC 1185(b), but fortunately there is no penalty for that.