"Eat crow" is an idiom that means to admit one's mistake or wrongdoing, often in a humiliating or embarrassing way. However, there are several synonyms that can be used in its place. One such synonym is "eat humble pie," which means to apologize or admit wrongfulness in a humble and contrite manner. "Swallow one's pride" is also a good synonym as it means to reluctantly admit fault or to abandon arrogance. "Admit defeat," "accept responsibility," and "face the music" can also be used as synonyms for "eat crow." Ultimately, the choice of which synonym to use may depend on the context and tone of the situation.