Exactly. As a med nin her chakra comtrol requires the utmost petfection if I may say and her loosing her kitten onlu means disturbace in the chakra flow, hence no chakra for healing hence dead Naruto.
There are a lot to take into consideration besides emotional impacg which is OBVIOUS either way. Can't forget her shocked face when she realized Naruto has no pulse. Zero heartbeat.
Put it this way, if Gaara never said anything about solution, she will lose herself. Gaara answered right away and Sakura became determined to do one last thing, which is more manual than she was doing. Honestly, we don't need tears all the time. Just when it's right. Plus, knowing Naruto love her is already enough. Crazy when you think she cries at thinking than just witnessing. Knowing Jinchuurki can die by extraction breaks her. Come on, isn't that enough.