The former Serbia boss replaced Delio Rossi at the beleaguered Genoese club last week and got his reign under way with a 1-1 draw against Lazio on Sunday.
Lorik Cana struck in the 94th minute to deny Mihajlovic a dream start at the Stadio Luigi Ferraris, and Mazzarri has claimed it is the "worst time" for his fourth-placed Inter side to meet them when they clash at San Siro this weekend.
"So far I've seen a little, I’ll study him more carefully these days," former Samp boss Mazzarri told Il Secolo XIX.
"The team seems to already be in good shape when you look at the players and now with Mihajlovic the team will have more fighting spirit.
"After a change of coach there is always a reaction and for us it's the worst time to meet them."
Mazzarri looked back on his time in Genova fondly, but insisted he would not be doing his old side any favours, with Inter able to overtake another of the 52-year-old's former clubs, Napoli, into the third and final UEFA Champions league spot with victory.
"The two seasons I spent in Sampdoria were exciting," he added. "We played well and achieved important goals. With a little luck, we would have won more.
"Inter is my present and I have brought my professionalism here. Today, I am an opponent, even if it feels strange."
