Reports had claimed Inter had rejected a loan offer for Perisic, which included an option of a permanent buy for €40 million in the summer.
But Spalletti believes the Croatia international was duped by the Gunners interest.
Speaking to Rai Sport after the defeat to Lazio, Spalletti said: "We've got to get Perisic back on track, but also Nainggolan, as he had injuries, setbacks and various issues. He needs time on the field and patience.
"As for Perisic, there was this story on the market, but he is a professional, understands his role and yesterday it was already a very different mood.
"These things happen in the transfer window, the player received an impressive proposal and was tempted. However, he then realised it was not a true offer, that he'd been conned, and took a step back.
"Now he'll resume training and as soon as his mind is back fully on Inter, we'll let him play."