Is Eat Crow equivalent to "Engolir Sapo"?

So, the OED definition of eat crow is "be humiliated by having to admit one's defeats or mistakes." Now, I'd say this is pretty close to the portuguese idiom "engolir sapo", which according to Priberam means "Aceitar uma contrariedade ou reconhecer um erro."

Is there a better equivalent for "engolir sapo" in English?