I think "I am responsible for the mistake" should be accepted too. I mean isn't it the correct translation? "pelo" = "por o" which means "for the". right?
Yes. "Fault" is actually closer in meaning to "responsibility" than to "error." Acceptable ways of using "fault":
I am at fault.
It's my fault.
The fault is mine. (unusual)
The way she pronounces "erro", is not correct for this sentence. Let's say we have two ways to pronounce this word: "êrro" and "érro" (both are written WITHOUT the accent). This sentence would require the first one (pronounced "êrro"), which is the pronunciation for the noun word "ERRO" ("error" in english). The second one "érro" (as pronounced in this exercise) is actually the first person singular (Eu - english I) conjugation in the Present Tense, as in "Eu erro" (pronounced "Eu érro), the verb being ERRAR, as in "to commit an error". Just remember that both forms are spelled without any accent, even tho they have different pronunciations.