There are several synonyms for the phrase "put at a disadvantage," which refers to being placed in a less favorable or inferior position. Some alternatives include "handicap," "undermine," "diminish," "impair," "weaken," or "hinder." These words all suggest a hindering or limiting effect on someone's abilities or opportunities. "Handicap" implies impediments that make it difficult to compete or succeed, while "undermine" suggests a weakening of one's position or authority. "Diminish" and "impair" emphasize a lessening of one's abilities or resources, while "weaken" and "hinder" suggest interference or obstruction in achieving one's goals.