Miguel Britos and Gonzalo Higuain put Rafael Benitez's side 2-0 ahead, before goalkeeper Pepe Reina saved a second-half penalty from Mario Balotelli.
The mercurial talent went on to notch an injury-time consolation, but the Naples outfit hung on for their first league win against Milan at San Siro for 27 years.
And Behrami believes the result was down to his team's hard work and togetherness.
"Tonight we had to work more and we suffered a bit, but we still secured an important victory," he told Mediaset.
"Milan will not be set back by this defeat. They had some absences and they also started badly last year, but ended up coming third. They will recover in the standings.
"Napoli have been more proactive this season, but more so in our other matches. Tonight we brought home the game with a lot of grit and character.
"In the second half, we couldn't keep the ball forward and lost it a lot very quickly."
The Swiss international was involved in an incident with Balotelli in the dying stages, with the latter receiving a red card after the game for dissent towards referee Luca Banti.
But Behrami played down the altercation, and insisted he was just happy the team took home the three points.
"He got mad because he called for a push on a shoulder to shoulder (tackle)," he continued.
"He did a little jump on purpose. Then he lost his head with the referee. He told me after the match that I did the push on purpose, but I told him I didn't.
"The refereee was there and explained that it was just a shoulder to shoulder and it didn't call for a punishment. I'm calm, however, he was agitated. We are very pleased with this win and will be happy to return to Naples."
