Milan could only finish eighth in Serie A last season, with Massimiliano Allegri and Clarence Seedorf failing to impress at the helm.
Inzaghi has been charged with the task of turning around Milan's fortunes and the former Italy striker got off to a winning start in when Lazio were consigned to a 3-1 league defeat last Sunday.
Fernando Torres, Marco van Ginkel and Giacomo Bonaventura have all been added to the squad since then, but Inzaghi offered a word of caution over Milan's hopes of being successful in his first season in charge.
"We must not run, we know what happened last year," Inzaghi told reporters.
"We must be realistic and clear, we are great enthusiasts but we must think game by game.
"There is a good spirit, the fans are back to being close to us, now it is up to us to do well, from the next match in Parma, which will not be easy."
Inzaghi expressed his gratitude for the backing he has been given in the transfer market during his reign so far.
"We have to thank the president and the club, for a transfer market that has brought us major players," he added.
"The latest arrivals, Torres, Van Ginkel and Bonaventura, are coups of excellent workmanship."
‘This is the hardest Manchester derby to call in years – Manchester United shouldn’t be petrified, it feels like Manchester City aren’t in control of any game at the moment’ Former Red Devils striker thinks a surprise result could be possible
‘Thierry Henry was my hero, but when you talk about players who have a wand of a left foot, he genuinely had that. He made my life so much easier on the right’: Ex-Arsenal star omits Gunners legend from his Perfect XI
