Missandei did not like that she had caused Daenerys pain, there were far more important things for someone of her stature to worry about. Not many saw the gentle side of Daenerys, but Missandei had and this was one of those times that it helped put her at ease.
As Daenerys explained the moment she witnessed Missande's death, she felt her heart begin to race again and anger rise within her. This was different from her initial reaction. While she had nothing to return to as she had died, there was a small hope within her that Daenerys would return and make Cersei pay for the pain she had inflicted on so many.