The Serie A giants moved five points clear in fifth with a 2-0 win at a 10-man Parma on Saturday that saw Rolando and Fredy Guarin score in the second half.
For the second match in a row, Inter goalkeeper Samir Handanovic saved a penalty, and his terrific save to deny Antonio Cassano just before the break with the score at 0-0 swung the match in his side's favour.
Mazzarri was quick to praise the Slovenia goalkeeper afterwards, but also called on his side keep their eyes on the prize.
"Handanovic did superbly, he prepares for penalties thoroughly," the former Napoli boss told Inter's official website.
"Guarin? I'm pleased for the lad, he really deserves it. I want more from this team.
"We have three tremendous games coming up against Napoli, the derby and Lazio, and then Chievo on the final day - and it's never easy to take points off teams scrapping at the bottom.
"We have to keep concentrating on each game as it comes."
Handanovic echoed his manager's thoughts, adding: "The penalty was an important moment in the match.
"We won, but some very tough games are coming. Nothing's been decided yet. We have to stay focused."
Goalscorer Rolando said that advice from coaches and team-mates saw him play a more active role at set-pieces - something that would pay dividends when he nodded in Hernanes' 48th-minute free-kick.
Rolando told Inter Channel: "It was a tough game but we played a good game and showed we're a team that should be playing in Europe.
"It's the hard work in training that's paying off. They told me to move up and I'd score, since I hadn't done it in a while.
"I'm happy, but the important thing is finding the right way to help out the team."
