Hamilton County Mayor Jim Coppinger said that the late-evening vaccinations happened because of that "miscalculation," which was compounded by the sheer number of people who drove to the vaccination site.

"[When] trying to balance the available vaccines with the number of people in vehicles waiting in line, we made some miscalculations," explained Coppinger, adding that the officials had to cut off the vaccinations at some point.

The health department also said in a statement that they didn't want people to "continue sitting in their cars and not get the vaccine because supply was limited." The department then asked people to leave and return for future openings, which were promised to be announced soon.

After dark, however, local news outlet WRCB went back to the site after getting a tip and found that there were still cars in the area. The people in the vehicles said that family members or friends who were helping administer the vaccines told them to come to get immunized. (Related: 5 Questions about the coronavirus vaccine that should scare everyone.)

One driver said when asked how he got the vaccine: "We have got contacts." The driver added that all seven people with him in the vehicle also received a dose. It’s not clear if these individuals met the health department's criteria of who should receive this round of available vaccines.

Vaccine's short shelf life forced officials to give vaccines to anyone

The people who were turned away were disappointed by the miscalculation, but health officials said that they needed to administer the vaccines no matter who gets them due to the short shelf life of the Pfizer-BioNTech vaccine.

"Because they had been thawed and prepared they had to be given by the end of the day. Our intent is to never waste any doses and we did not waste any Thursday," said Barnes.

Coppinger also clarified that the health department's main priority is to ensure that the vaccine supplies do not go to waste and so must be administered to willing recipients. As such, staff members called people who requested the vaccine or were unable to be vaccinated at a previously scheduled time. (Related: The media will HYPE the coronavirus the day a VACCINE is available.)

Though grateful that none of the doses went to waste, the people who were turned away were disappointed by how the situation was handled. Kelley McCahill, who waited four and a half hours before leaving the site when it was shut down, said that seeing other people get vaccinated instead of those in line was "a slap in the face."

"I'm glad those people got (the vaccine) ... I'm just really, really frustrated that I waited all that time with the physical issues," said McCahill who has health problems. She hopes that administrators would learn from Thursday's mishap and figure out a way to make the process easier for everyone.

Coppinger said he is expecting a new vaccine supply this week. He added that his administration is considering putting up another vaccination site and has been discussing ways to improve traffic flow and calculations.