Despite the late signings of Brazil international Hulk and Belgium midfielder Axel Witsel in the summer transfer window, Zenit have only won once in five games, culminating in the Champions League defeat to Malaga, and the 2-2 draw to Kryliya Sovetov on Saturday.
Spalletti, who steered Zenit to the Russian Premier League title in 2010 and 2011-12, has insisted that the team will bounce back, and that "everything will be alright".
"The fact is that the team isn't calm mentally, because some players feel that it's the right thing to be upset right now," the Italian trainer told the club's official website.
"They need to understand that the way they're thinking isn't fair. But after what I saw today in the second half, our fans can be rest assured, that everything will be alright.
"I said last season, that if we don't win the championship, then I'm leaving. Considering that a situation has taken shape now which I don't like, I'll tell you honestly, I get pleasure from such difficult situations.
"Now, I'll tell you that I won't leave until Zenit fires me. I have a contract for three years. And I'm going to work at our training facility from nine in the morning, until five-six-seven or eight in the evening."
Spalletti's side sit fourth in the Russian Premier League, four points behind CSKA Moscow.