What "being responsible" means is quite dependent on your situation.
If you were generally quite well in the community that might mean making a gp appointment when you notice things start to slide.
If you were less well in the community that might mean reaching out to crisis support when needed.
In a hospital setting that might be speaking to a member of staff when needed.
It is easy (I know I've done it!) to take offense when someone suggests you need to take responsibility, we jump to the top scenario and how we could cope when generally doing OK but its actual meaning and intent could be wildly different.
Would it be helpful to find out what they actually meant by "take responsibility" even if it something that isn't manageable right now it might be something they could help you work towards.