Inter were comprehensively outclassed by Carlo Ancelotti's Napoli at Stadio San Paolo on Sunday, only becoming a genuine threat in attack once they were 3-0 down away from home.
Piotr Zielinski's stunner was added to by a Dries Mertens header and Fabian Ruiz's brace, with Mauro Icardi's consolation coming via a late penalty.
Inter could have confirmed Champions League qualification with victory, but failure on that front means they head into the final game of the season just a point ahead of bitter rivals AC Milan, who beat Frosinone 2-0.
Goals from Krzysztof Piatek and Suso secured victory for the Rossoneri to take the top four race to the final weekend.
Spalletti's side face relegation-battlers Empoli at home in their season closer and the head coach has thrown the gauntlet down to Inter's players.
"It's a final for us, we need to be ready to play it," he told reporters. "We need to maintain the composure of those who know how to assess things.
"The team played poorly [against Napoli], but our destiny is in our own hands. We need to take to the pitch to win because it's a crucial match for us, we'll either be in or out.
"We need to have the substance, composure and strength that an Inter side should have. You have to know how to withstand this kind of pressure if you wear this shirt."
Inter were given a boost earlier this week when it was confirmed they had been released from the long-standing sanctions imposed on them as party of their Financial Fair Play (FFP) settlement agreement.
The club were punished with heavy fines and limited to a squad of 21 players in the Champions League this term, down from the usual 25, after breaching FFP regulations in May 2015.
However, the UEFA Club Financial Control Body (CFCB) say they "have been considered in compliance" with their agreement so have now had the restrictions lifted.