The result left second-placed Inter on 39 points from 18 matches, 10 points behind Juventus, who beat Palermo 2-1 on Saturday.
AC Milan, third on 37 points, can climb above Inter by beating Parma at the San Siro stadium in a later match (kickoff 1930 GMT).
Inter had racked up six consecutive wins leading up to the Christmas break.
There seemed little reason why they could not extend their run at Siena's Franchi stadium against a side that had lost more games than they had won at home this season.
Despite lacking urgency in the first half, Inter enjoyed greater possession and twice went close to taking the lead as Dejan Stankovic headed narrowly wide from a corner and then an Adriano free kick flew just the wrong side of the post after deflecting off the wall.
Inter upped the pressure in the second half but let a series of excellent chances go begging.
Stankovic blasted Giuseppe Favalli's cutback directly at keeper Antonio Mirante on the hour.
Four minutes later, the Serbia and Montenegro midfielder failed to turn Adriano's low cross into the net from close range.
He made up for his mistake soon afterwards with a precise cross to Obafemi Martins, who was unmarked in front of goal, but the striker headed over the bar.
As the match neared its end, Inter coach Roberto Mancini brought on a third striker, Alvaro Recoba, and replaced Adriano with Julio Cruz in the hope of breaking the deadlock.
The tactic failed to pay off, however, and in the final minutes Inter lost their momentum.
Striker Cristiano Lucarelli scored twice as Livorno beat Sampdoria 2-0 to notch up their fourth win in five games and consolidate fifth place in the division on 34 points.
Sixth-placed Chievo Verona beat Lecce 3-1 to move on to 30 points.
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