My high functioning ASD 9 year old has a lot of rejection sensitivity issues, so failures and disappointments cause a lot of big feelings and big reactions.

I think that your measure for harshness might need to be in context of your actions, and not her reactions.

Maybe you can talk to her about being proud or happy that she realizes how her actions were but appropriate, and that we're always learning new things. But, she might also feel to embarrassed to want to talk about it

Maybe you can approach the subject with her to gauge her receptiveness to revisit the incident, and maybe conduct a sort of debrief to reinforce and support her realization that what she did was wrong, framing it as you being sorry that she feels so bad about it, but that you're proud that she's learned something new, and that her big feelings about feeling bad means that she is truly a good, well meaning person.