Simone Vergassola opened the scoring for Siena before a Max Tonetto own goal doubled their lead, Mario Frick completed the rout in the final ten minutes.
"It looks as if our minds simply weren't on the job, because in the second half the team reacted and showed the qualities we need," barked Spalletti.
"Siena had desire and focus, so even if the table says we are the stronger side, we weren't ready to fight them on those terms."
It is the latest setback in the Scudetto race and leaves Inter eight points clear despite closing the gap to five points last weekend.
"If we have these stumbles on a regular basis, we cannot aim for a particularly important trophy, because this makes the difference. Siena fully deserved their victory."