Managers should enable and support teams in doing retrospectives. They can ask and expect teams to improve within the possibilities and constraints of the organization, and contribute to the organization's goals, but it is up to the team to choose how they improve and where they decide not to improve (now).

Who Should Participate in a retrospective?

Who Should Attend a Sprint Retrospective? Sprint retrospectives are for the Scrum team, which would include the development team, Scrum Master, and Product Owner. In practice, product owners are recommended but not mandatory attendees.

Should product manager be in retro?

AFAIK Product Manager/Owner decides the priorities of the User Stories. So, he/she should attend the Scrum retrospective to learn what needs to be improved and meet target goals.