What will they think?

Today, I made a mistake while performing my job. I sent some incomplete information while sending an e-mail. I realized shortly after the mail was released. I apologized to the concerned person and wanted to release the corrected mail.

Till I modified and sent the revised mail, I was so restless with myself. I was guilty of my mistake. Such silly mistake while sending such important information? What will they think??

There I am...what will they think? All the restlessness in me was because of the fear of what will they think or because of the realization that I made a mistake? Is it okay to constantly think what will others think? Do I need to be self-critical?