Of course is the duty of the manager to make sure that his boys conform to his plan or strategy and if something goes wrong he should be able to take the blame, though I no that in most cases players go against the strategy instructed by the coach but still he has to take the blame because they are paying him to use his coaching skills and improve the performance of the club, so perhaps any coach that's always fund of taking excuses of his failure will always be replaced by another.
In the case of Ten Hag one thing he must understand is that before he joined the club Manchester United was doing very well, though even if they weren't that perfect but they were more better then than now, so is obvious most of there problems are coming from there coaching pattern, imagine they could not even qualify for the champions League this coming season, well let's see if they will improve next season.
Managers who take the blame are great managers, there are managers out there who blame the players and I hate those type of ones, because that is not good leadership and if you blame your players, even if one of them, then the rest of the squad will not see you as their leader, they will see you as traitor and they will not trust you because tomorrow you can blame another player who knows.
Erik Tan Hag has this issue for example, he has openly talked about some players, like Sancho for example, and how does he expect some of the players to trust him, how does other United players are so sure that they won't be next in line of the target? They cant be, some like Antony will continue liking him because he gave opportunity he doesn't deserve, but that's it.