Milan secured a 0-0 draw with second-placed Roma at Stadio Olimpico on Saturday, despite playing the closing stages with 10 men when Pablo Armero was sent off in the 71st minute.
That draw followed an impressive 2-0 triumph over Napoli last weekend and Milan head into the mid-season break seemingly well place to challenge for a UEFA Champions League spot.
Head coach Inzaghi certainly believes that an assault on Europe's premier competition is doable and praised his team for their recent performances.
"I'm thrilled. I was hoping to win," he told Sky Sport Italia. "This team makes me so proud.
"With four points from Napoli and Roma this gives us confidence. We are on the right track.
"Now the growth [of the team] should be gradual. With this spirit we can get to third place."
Inzaghi stated that he felt the red card for Armero - which came for a second bookable offence for deliberate handball - was harsh, while he also praised the performance of goalkeeper Diego Lopez, who made a series of fine saves.
"The red card of Armero seemed excessive," he added.
"[Real Madrid coach Carlo] Ancelotti told me Lopez was a great goalkeeper. He also advised us on [Jeremy] Menez so we must thank him."
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