to undergo the humiliation as of having to retract a statement or admit an error
See full dictionary entry for crow
eat crow
to admit that you have been wrong and apologize, especially in a situation where this makes you feel ashamed. The usual British expression is to eat humble pie.
But by the end of the year, Safire showed he was willing to eat crow. His first judgmentsof Watergate, he wrote, had been `really wrong'.