The Nerazzurri came close to beating Atalanta last time out but, after Mauro Icardi missed a golden opportunity to win the game for Inter, Giacomo Bonaventura raced up the other end to make it 2-1 to Atalanta.
Other results left the ambitious Milan outfit stranded in sixth place and they risk losing ground on upwardly-mobile Parma if they fail to put 14th-placed Udinese down at San Siro.
Mazzarri told inter.it: "Our match with Udinese is laden with pitfalls - just like the Atalanta game was.
"It's tough against certain teams and certain coaches because they're very good and because they know how to make things difficult for you, being able to play for two out of three results.
"Inter are used to facing games like that. We'll have to be better, and a bit more lucky, at taking the game to them from the off and trying to get an early goal.
"I expect to see a lot more concentration against Udinese. We mustn't give anything away, remain calm and take the right option when we get the chance."
Defenders Cristian Chivu and Marco Andreolli are sidelined through injury while Udinese arrive in Milan without suspended midfielder Dusan Basta.
The Bianconeri have failed to win away from home in four attempts but plundered a surprise 5-2 victory in this fixture last season.
That means nothing to visiting coach Francesco Guidolin, however, and he is suitably wary of a backlash from Inter following their disappointing weekend.
"We are expecting a loud and angry Inter," he told udinese.it.
"They are a strong and improving team that has made some significant steps forward lately.
"We need to focus and show both strength and the desire to counter our opponents blow for blow.
"We'll go out onto the pitch looking to get the best possible result, as always."