The 51-year-old is refusing to underestimate AC Milan in the race for second while he also cools speculation on Edinson Cavani's future
The Partenopei's 1-1 draw at AC Milan last weekend ensures they sit four points clear ahead of their close rivals for automatic Champions League qualification next season, but the Italian is refusing to relax yet.
"I hope they do not take second place for granted. AC Milan could win all its games, looking at the fixtures. They could even beat Juventus," Mazzarri told reporters before the match.
"I do not want my team to believe, as the media say, that second is ours. I do not want them to consider this match against Cagliari less difficult than the one we played at San Siro.
"We must think only about our performances. It is high time we accelerated and initiated a turning point to achieve qualification for the next Champions League."
Serie A top scorer Edinson Cavani has often been linked with a move away from the club, but Mazzarri insists his star player is only concentrating on ending the current campaign on a high.
"I've become accustomed to people talking about us. I do not think Cavani is thinking about anything else. He just wants to finish this season in the best way possible," he continued.
"He always trains and gives his all. I am not the person you need to ask about his future."
The Uruguay international has already registered 22 goals in 29 league appearances this term.