Victor Ibarbo scored a hat trick last week against Sampdoria and he looked set to get on the scoresheet again when he used his pace to burst into the area, but Siena goalkeeper Gianluca Pegolo raced off his line to close down his shot.
Radja Nainggolan thumped the follow-up wide.
Siena came into the game in the second half but struggled to carve out any quality goalscoring opportunities.
Cagliari appealed in vain for a penalty when Angelo appeared to bring down Ibarbo, but the referee waved play on.
Siena, which started the season with a six-point penalty following a match-fixing scandal, is now one point from safety.