Parents said they wanted the teacher's name so they can determine if their child was in the teacher's classes, but military officials refused.
"There's no way for us to know who the teacher was or what classroom they were teaching in," complained one parent.
Parents also expressed anger that they were only finding out about the allegations now when the teacher was fired back in November.
"So here we are in March, and a lot of people are wondering who dropped the ball," said another parent.
Base officials first alerted parents last week in a letter.
The letter from Col. Stephen Sicinski -- Fort Bragg's garrison commander -- was sent to parents of students attending McNair Elementary School on Honeycutt Road on post.
The male teacher worked at seven different schools over a two-year period. Officials said the incidents in question involve male and female students and happened at multiple schools, but they declined to name specific schools.
Parents were told Friday that of 14 allegations against the teacher, two have been substantiated.
No charges have been filed. The investigation is ongoing.
A hotline has been set up by Fort Bragg for concerned parents. That number is (910) 907-6680.