Inter have 59 points from 27 games after their fourth draw in five league games and maintain the four-point lead they started the weekend with over Milan, who failed to turn dominance into goals in another goalless draw in Rome on Saturday.
AS Roma are three points further back in third.
Nevertheless his team were sterile in attack in a listless first half, when Genoa's Giandomenico Mesto and Giuseppe Sculli and Inter's Dejan Stankovic all had crisp but central shots easily saved.
The champions made three substitutions in a bid to shake things up after the break with the struggling Samuel Eto'o among those making an entry from the bench.
"We had a lot of players who travelled and played 90 minutes with their national teams this week," Inter's technical director Marco Branca told Sky television. "You cannot always be at the top in terms of concentration and desire.
"It's a point and it's one game less to the end of the season. Today's match wasn't brilliant. That can happen during the course of the championship."
Palermo regained fourth place earlier on Sunday when Fabrizio Miccoli's late goal gave them a 1-0 home win over relegation-threatened Livorno.
Stefano Guberti's piledriver and a volley by Giampaolo Pazzini clinched it in the first half after Sergio Floccari's early opener for the Rome club.
