The phrase "hadst a part in" typically implies involvement in a certain action or event. Some antonyms for this phrase could be "uninvolved", "disassociated", or "distant". If someone did not have a part in something, they can be described as being "removed", "excluded", or "unconnected". On the other hand, if someone actively avoided participation in a situation, they can be labeled as "disengaged", "withdrawn", or "aloof". It's important to consider the context in which these words are used, as they can have varying degrees of implication regarding the level of involvement or detachment from a certain action or event.