Petev's unveiling on Tuesday descended into farce when furious Levski followers forced the 38-year-old to remove a shirt bearing the club's logo and leave the room, claiming he was a supporter of fierce rivals CSKA Sofia.
Despite the humiliation, Petev - the winner of consecutive A Football Group titles with league leaders Ludogorets - initially expressed a desire to continue in his new role.
However, he has changed his mind after discussing the situation with his family.
In a second news conference, Petev said: "What happened yesterday is extremely ugly and I would not like to work in such an environment.
"I wanted to work at Levski but I didn't expect that such a thing could happen in the 21st century.
"This is something abnormal. I'm not a criminal; I'm not a thief, but yesterday I felt exactly like that."
It had previously been reported in the Bulgarian media that Petev was a CSKA fan, but he added: "I did not say this. I have no sympathy for another Sofia club."
Petev has been replaced by former Levski defender Antoni Zdrakov, whose first game in charge will be against CSKA on October 19.
"The team will be coached by Antoni Zdravkov until the end of the year, at least," Levski owner Todor Batkov said.
