Rodrigo Palacio and Jonathan found the net as Inter recorded a 2-0 victory at Verona on Saturday to climb to fourth in Serie A and two points clear of Fiorentina, who face Chievo on Sunday.
But coach Mazzarri will not get carried away after a run of form that has seen Inter go six games unbeaten.
"We talk the way we always have done, that every game has to be played the same way whether home or away, then at the end we'll see where we are," he is quoted as telling Sky Sport Italia. "That's the objective for this season.
"I've tried to drill into these players from the start that they must go for the win from the very beginning and maintain the same mentality no matter where they are playing. That means winning back possession as quickly as possible and seeking the victory every time.
"You can see that in recent outings the team has indeed taken that approach.
"In the past when we've taken the lead, we have settled down and the players know I don't want them to have that attitude when the game is still open. I therefore told them to act as if it was still 0-0."
Hernanes and Mauro Icardi both hit the crossbar for Inter and Mazzarri revealed he had long been an admirer of the former before signing him from Lazio in January.
"If we wanted him, it's because the club asked me who could be useful and I'd already asked for him at Napoli," he continued. "I always liked this player and I think he can do even better, as he's not at 100 per cent yet.
"He keeps calm and controls the ball with characteristics we had been lacking."
Mazzarri also moved to address doubts surrounding his future that surfaced during the week.
"Next season I will certainly be the coach, as I have a contract until 2015," he added. "Someone tried to twist my answer this week, as I was discussing contracts and said there was time until June to extend or discuss, but it's the last of my worries right now because we have to focus on the team.
"It is only by getting results that we can plan a bright future and that includes any discussions over my contract extension. That's all I said."
