Goals from Goran Pandev and Blerim Dzemaili ensured the Azzurri remain within nine points of Serie A leaders Juventus - despite Edinson Cavani's missed penalty - with Milan now trailing by four points ahead of Sunday's meeting at San Siro.
Juve may well prove to be out of reach for Mazzarri's men with only seven games left to play, but guaranteeing a place in the Champions League group stages would represent another successful season in Campania.
He told sscnapoli.it: "We deserved to win, we are back to our level.
"We don't look at our opponents, we just have to concentrate on ourselves. We have won three matches in a row and that means a lot.
"We played a good game against Genoa because they had quality and physical strength, so our approach was the right one and we managed to make the most of our chances from the beginning.
"From [Monday] we will start thinking about AC Milan. You know that these kind of matches are unique and from a psychological point of view there is no need to talk about specific preparation.
"AC Milan have enjoyed a great revival and we are aware that this is going to be a tough game. We will have to be as brilliant and determined as we are now.
"Let's focus on these last few matches to emphasise our extraordinary season.
"We have got 14 points more than last year and we want to qualify for the Champions League again - that would be an extremely important achievement."
Genoa, however, are facing relegation to Serie B after slipping into the bottom three on the back of a fourth defeat in five games.
The Rossoblu are tied on 27 points with Siena and Palermo but have the poorest goal difference of the three.
Head coach Davide Ballardini told La Repubblica: "Have I had a vote of confidence? We've not talked about it.
"We've talked about the future in relaxed terms and about how we'll use the last few games to book our survival.
"Genoa are in good shape. The results have not been good but the overall state of things is fine. I am convinced Genoa have the means to get out of this situation."