Andreas Granqvist grabbed an equaliser but Genoa could not find the winner they desperately needed to see off fellow strugglers Torino and improve their position towards the foot of Serie A.
Sweden international Granqvist nodded home after 29 minutes to cancel out Rolando Bianchi's opener for the visitors.
But Genoa could not conjure up a second, although they did have a goal chalked off two minutes into the second half when Marco Rossi was adjudged to have been offside when he poked the ball home.
Having won just three league games this season, a home fixture against a Torino side who started the day three points and three places better off would have been viewed as an opportunity for Genoa to improve on 19th position and edge closer to safety.
And they made a promising start, with only a fine save from Jean Francois Gillet denying Marco Borriello from the edge of the area. The rebound fell to Ciro Immobile but he shot wide.
Genoa then fell behind following Torino's first attack of note after 19 minutes.
Valter Birsa whipped in a wonderful cross from the right and Bianchi got in between two defenders to direct a header past home goalkeeper Sebastien Frey.
Genoa were level within 10 minutes, though, Granqvist nodding home from inside the six-yard box following a corner.
The only other chance in a disappointing first half low on quality fell to Borriello four minutes before the break but the on-loan Roma striker fired high over the bar.
The hosts felt hard done to at the start of the second period when the assistant referee's flag denied Rossi after Gillet could only parry Immobile's volley into his path.
And they threatened once more midway through the half when Granqvist shot over when well placed.
From there on in, however, it was Torino who looked the more likely side to grab a winner.
Bianchi shot over after 65 minutes, while Alessandro Sgrigna hit the bar from a similar distance 14 minutes later.
And with four minutes to go, Giuseppe Vives' firm header flashed inches wide with Frey a spectator.