Dzeko stormed off after he was substituted during Roma's 4-1 win, abusing Spalletti before storming away to the locker room.
Spalletti said: "Dzeko? I didn't realise that Dzeko had told me 'to be smart again'? I went into the dressing room and greeted everyone as usual.
“Now I'll try to fix this because I didn't notice any of it. He looked angry… Luckily, he went to the bench right away!
“Being the only striker I have, I'd say that without him, I'd never want to play. It wasn't an act of rudeness.
“I took him off because he's the only striker that's played all year round. Emerson began to struggle and I had to take him off, as I did Paredes.
“I'd have taken off those in front of them otherwise, Dzeko, Salah, El Shaarawy, because I only have a few players in attack. it's a preventative reading."