On Tuesday, the Lakers announced their roster were currently symptom-free after two players contracted COVID-19 amid the pandemic, which has brought the NBA and sport to a standstill across the globe.
The Lakers, on March 19, revealed a pair of unnamed players tested positive for coronavirus, but after completing a 14-day home isolation, no Lakers players showed symptoms.
However, Vogel told reporters via a conference call on Thursday: "To my knowledge, the rest of the staff was not tested.
"The only people that were tested upon the news of the Brooklyn Nets' positive test results were our players.
"That was ... following the lead of our team doctor and the local health officials."
Vogel added: "It's just, we were not told to be tested. And obviously everybody recognised the shortage of tests and we were only going to do what the local health department told us to do. So, we weren't asked to be tested at that point.
"I reassured my family that I was in good health and obviously, while I had been around those guys, there had been some social distancing guidelines in place, so I felt fine and I also felt confident that a test wasn't needed for me personally. But I think everybody is in a case-by-case basis with that."
Confirmed cases of coronavirus have exceeded one million globally, with more than 53,200 deaths.
In the United States, over 6,000 people have succumbed to the virus from at least 245,190 cases.