以下の使い分けをすれば良いと思います。
〇 be disappointed with＋人・物 人・物にがっかりする
● be disappointed at＋物　物にがっかりする　×be disappointed at＋人

【参照】
[Cambridge Dictionary]
We were deeply disappointed at/about the result(物).
His parents were bitterly disappointed in/with him(人).
[Oxford Learner's Dictionary]
disappointed at something(物)
disappointed with somebody/something(人・物)
[Longman Dictionary of Contemporary English]
disappointed at/with/about something(物)