"I want to make it absolutely clear - I will not quit even if we lose to Basel," he told reporters on Wednesday ahead of Thursday's Europa League last 16, second leg tie against the Swiss side at St Petersburg's Petrovsky stadium.
The Russian champions must overturn a 2-0 defeat from last week's first leg. It was Zenit's third consecutive defeat in all competitions and football pundits have led calls for the Italian's exit.
"I think Spalletti has exhausted himself at Zenit. You can see it by just looking at him - it seems he just doesn't have the fire anymore," former Zenit and Russia striker Alexander Panov was quoted as saying in Tuesday's Sport-Express daily.
Zenit lost to Liverpool 3-1 in last month's Europa League last 32 tie but scraped through to the next round on the away goal rule having won the first leg 2-0 at home a week earlier.
"Of course, if you don't get results your role as a coach is in doubt. It's a normal thing in football," said Spalletti, who has led Zenit to back-to-back Russian league titles in the last two years.
"I'm not a quitter, I know that we can change this situation around," said Spalletti, adding that first-choice goalkeeper Vyacheslav Malafeyev will miss Thursday's match against Basel with a back injury.
