Edin Dzeko scored twice in Roma's 4-0 rout of Fiorentina on Tuesday, which helped the Italian capital club move into second in the table.
Roma are four points adrift of defending champions Juventus, who have a match in hand.
But after watching the New England Patriots overcome a 25-point deficit to beat the Atlanta Falcons 34-28 in NFL's Super Bowl LI on Sunday, Spalletti has belief.
"We are having a great season, so are Juventus and Napoli," Spalletti said via Mediaset Premium.
"It is our duty to believe to the end, as there's this spell with many games that could create some surprises.
"Look what happened in the Super Bowl. We have to believe."
Dzeko led the way for Roma at the Stadio Olimpico as the Bosnia-Herzegovina international took his Serie A tally to 17 goals this season.
No Serie A player has scored more league goals this campaign after Dzeko opened the scoring and added gloss to the scoreline with seven minutes remaining.
"I don't need say anything to him because he's on a high and everyone is behind him again. Then when he misses a chance, they all abandon him," Spalletti added.
"There's no need to say anything to him because he'll get plenty of positive messages after a game like this."