Acerbi, 37, played the full 90 minutes for Inter Milan as they suffered the biggest defeat in Champions League final history against PSG on Saturday.
Just hours after the 5-0 defeat, he got a call from Spalletti, asking the centre-back to represent Italy in their World Cup qualifiers against Norway and Moldova.
He rejected the chance, however, later turning to social media to explain his reasoning to a slew of disappointed fans.
The veteran defender said: "It's not a decision I have taken lightly. However, I believe that in light of recent events the conditions aren't there today for me to go forward with serenity.
“I demand respect. If that respect is lacking from those who should lead the group, I prefer to step aside. I won't stay where I'm no longer truly wanted and it's clear I'm not part of the coach's project."