A late Luca Antonelli header was enough to seal victory for the hosts at a rain-soaked Stadio Comunale Luigi Ferraris - their first triumph over Inter since 1994.
And coach Gasperini, who was in charge at Inter for just a few months in 2011, hailed the spirit and commitment of his team.
"It was a good game in tough conditions, as there was so much water," he told Sky Sport Italia following his first victory against his former employers.
"Inter are a physical side, but Genoa really did well and played with intensity, and this victory means a lot to us.
"Without doubt the stadium and these fans help the team and give us something more, especially when we play with this hunger.
"I think at the end of the day we were on a par with Inter throughout and had our good chances to score, as did they. As the conditions got worse, we both had to sort of throw the ball into the box and hope for the best.
"I believe our desire to win was decisive."
Gasperini had spoken ahead of the match about his difficult spell at Inter and appeared to suggest that the club had benefited from the Calciopoli scandal in 2006.
However, he sought to explain his views after Sunday's encounter.
"Even if I wasn't there for long, I maintained a rapport of great respect and admiration with the Inter players," he said. "I have always tried to push forward and continue to respect them.
"I was asked about difficulties coaches had at Inter and I said in the last 15 years or so the only ones who have done well there are Roberto Mancini and Jose Mourinho.
"I don't think it is offensive as, other than them, great players, great coaches, mediocre player and mediocre coaches - all seemed to make no difference.
"The only time any coach managed to really do something good at Inter was straight after 2006. I'm sorry if they got angry, but there were many really nasty things said that wasn't to do with Calciopoli."
