"Eat one's words" is not similar in meaning to "put one's foot in one's mouth" -- although if you put your foot in your mouth (say something really inappropriate or awkward) you might eventually have to eat your words (humbly retract something you proclaimed confidently).
Hi, While it is not an idiom in English, the French faux pas [= false step] meaning a blunder in manners could be used in place of 'put one's foot in one's mouth'.