I think Mikasa looked a bit sad until Louise brought up the whole Eren thing and made it look like the scarf holds nothing special. Then Louise started talking as though Mikasa is her Eren. I think Mikasa saw the dishonest and futile nature of that belief.

I think Louise reminded her of a part of herself that she doesn't like anymore. She doesn't want Louise to see her as her Eren. Louise followed Mikasa without even knowing who Mikasa really is and says she has no regrets about it. The harshness with which that scene was depicted tells me that way of living is not a good one. And Mikasa knows it. It can be interpreted as her correcting the young girl's path on her deathbed with the harshness that is truth. And that's just my interpretation. She came off as a cold yet wise woman. I personally loved the scene. Sad, but eye-opening.