The definition I found of sarcasm is the following:

"a sharp and often satirical or ironic utterance designed to cut or give pain"

I think the response I'm complaining about is satirical, so I think it matches sarcasm by this definition.

Anyway, even if hadn't been sarcasm, technically, it seems mocking and unkind. And it's not a big deal, but I think my response of "I don't appreciate that" was pretty tit for tat.