Rodrigo Palacio and Andrea Ranocchia both scored from set-pieces midway through the first half in Udine, before Palacio set up Ricardo Alvarez in second-half stoppage time to seal a win that preserved their unbeaten away record in the league this season.
Inter sit fourth, six points adrift of Juventus in third, but Mazzarri urged his side not to be distracted by what other teams are doing around them.
"I've told my guys that we should only be focused on ourselves and not on the other teams," he said.
"As of now we should only be focused on this. The other teams have different features and have a different history.
"We have to be focused on ourselves and then we'll see the results at the end.
"This is our new beginning, there has been a big change in the club, and last year the team closed the championship in a certain way.
"Therefore we only had to find an identity and be competitive as soon as possible.
"I know that these guys understood very quickly the type of game that I wanted from them and the ideas I wanted them to express on the pitch.
"Of course we know that we wasted a few points due to the mistakes we made, but this is part of the improvement process.
"We're a young team and many players weren't used to playing as regular players in such an important club."
Mazzarri went on to praise his opponents, who have now lost three of their past four matches.
"I watched the match that Udinese played against Roma and I believe they didn't deserve to lose," he said.
"I have to say that I was afraid of Udinese because this team is made of skilled players and has a great manager, therefore this match was difficult under every point of view.
"I believe we made a good job and didn't let Udinese express their way of playing. We put many pressures and didn't concede almost anything.
"We had two or three good occasions even before scoring our first goal. Therefore I believe we should be praised if Udinese didn't manage to play as they are able to play."
