There's something very striking to me about how Rose acts in 'The Patient'. She says to Oscar that they have more important things to worry about, then reveals at the end that seeing Carrie act that way "brought back some painful memories". Even though her tendency to prioritise the mission over personal issues doesn't really shine through in Series 3-5 as much as it did in Series 1-2, it still might be there on some level.
It's why she redirects what she saw as a personal failure back in 'Moontaker'—one that almost prevented them from carrying out the mission—onto Carrie, because it's how she viewed that experience once she came out of it. Even though Rose does value the team format, she tells Carrie, "If you can't pull yourself together, we're better off without you." She sees Carrie's behaviour as interfering with the mission, and she can't work with Carrie if she struggles to follow their plan and can't set her feelings aside.
That's why Rose later says she let the team down when she wasn't there for Carrie. Being in a team doesn't necessarily mean that you always handle missions successfully, but that you look out for the other people that you're with to accomplish that goal, and I think it's nice that Rose comes to that conclusion.