The incident, which was missed by match referee Davide Massa and his fellow officials, occurred in the 33rd minute of the Serie A contest at the Stadio Sant'Elia on Sunday.
Destro scored a hat-trick in Roma's 3-1 triumph and has now netted seven goals in his last five matches.
But Roma's remote title chances will be further blighted by Destro's absence after a video review of the clash between the 23-year-old and defender Astori revealed wrongdoing on his part.
Serie A's governing body have handed him a three-game ban and an additional one-game sanction for the number of yellow cards he has accumulated following a caution in the 42nd minute of the clash in Sardinia.
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