The Potters had plenty of chances to beat their Italian opponents, but instead had to settle for a fourth successive clean sheet in pre-season.
Peter Crouch almost gave Stoke the lead after just 10 minutes, but his header struck the post following a fine ball from Jon Walters.
The same players linked up again on 25 minutes, this time Crouch was the provider, but his knock-down was fired straight at Genoa keeper Mattia Perin by Walters from six yards out.
The Premier League side created another opportunity on the half-hour mark as Geoff Cameron and Crouch combined for Steven N’Zonzi to fire wide when Walters was better placed.
And before half-time, Stoke came close again when Robert Huth’s header forced a fine save out of Perin.
The second half failed to match their tempo of the first, but it was a pleasing performance for Hughes ahead of his first competitive fixture in charge of Stoke at Liverpool next weekend.