In a statement, Applewhite congratulated Mayor-Elect Nat Robertson.
"This has been an extraordinary election and a wonderful experience. Less than 250 votes out of over 22,000 cast separate my campaign from victory. I thank each and every person that poured their energy into my campaign and believed in my vision for our city," said Applewhite in a statement. "We have examined the election returns and have determined that under the best of circumstances, the likelihood that a recount will change the outcome of the election is slim. I accept the finality of the results and offer my congratulations to Mayor-Elect Nat Robertson."
Applewhite served on the city council since 2007.
The two were the top vote getters in October's five-candidate primary. Robertson replaces Mayor Tony Chavonne, who chose not to seek a fifth term.
Robertson will be sworn in next month.