The phrase "hadst a hand in" implies involvement or participation in a particular event or situation. Its antonyms could be words or phrases that indicate the opposite, such as "had no involvement," "had no connection with," "was not involved in," "wasn't implicated," "wasn't associated with," or "had no part in." These antonyms signify a lack of responsibility or accountability for a particular action or outcome. By using antonyms for "hadst a hand in," you can clearly express that someone was not involved in something or was not responsible for a particular outcome, thus avoiding any confusion or miscommunication.