I realized that I had not been assigned a role as the person in charge.
ご質問ありがとうございます。
「私がその担当に割り当てられていなかったことに気づいた。」は英訳すれば、「I realized that I had not been assigned a role as the person in charge. 」になります。
具体的のケースを英訳するともっとわかりやすいと思います。下記の通りになります。
「For the period between June 1st to June 10th, I didn’t happen to realize until June 9th that I had not been assigned a role as the person in charge. 」一つ目の英文に基づく、二つ目の英文を作りました。
ご参考になれば幸いです。