Lazio had overcome visiting Milan 3-1 in Serie A on Saturday and three days later a penalty from Lucas Biglia gave Stefano Pioli's men victory on the road in the Coppa Italia.
Reports in the Italian media continue to claim that Inzaghi is on the verge of being sacked with Milan sitting 11th in Serie A, 10 points off the UEFA Champions League places.
But the 41-year-old, who was only installed as coach in June, is convinced he deserves more time to rebuild Milan.
"When you open a new cycle you need patience," Inzaghi told Milan Channel after the loss.
"We have to try bit by bit to get back to what we always were. With this playing system we need another forward."
Inzaghi added he is excited by the prospect of securing Spartak Moscow defender Salvatore Bocchetti on loan: "I am aware of Bocchetti and I like him a lot as a player.
"Bocchetti is a profile that could interest us for his versatility and he is left-footed. If it goes well he could be a good purchase."
Bocchetti is reportedly scheduled to complete a medical with Milan on Wednesday.
While Milan's scoring woes continued at the San Siro - they have scored just one goal in their past three games in all competitions, coinciding in three consecutive defeats - Inzaghi was bullish about his team's attacking set-up.
Giampaolo Pazzini and Alessio Cerci both hit the back of the net on Tuesday but the referee disallowed their goals.
"The goals did come tonight, there were two of them," Inzaghi said.
"I am very happy with my team tonight, while on Saturday I wasn't. Tonight the result doesn't reflect the match, we gave our all, the match incidents were never in our favour.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.