Carlos Tevez scored 19 minutes from time at San Siro to ensure maximum points for Juve and Massimiliano Allegri - the coach making his return to Milan having left the club in January.
The result ends Milan's 100 per cent start to the Serie A campaign but Inzaghi was far from downbeat in his assessment.
The former striker - who represented both Milan and Juve in his illustrious playing career - feels his side are not far off the level of the Turin club, and called on his squad to continue improving after a disappointing eighth-place finish last term.
"We have to move forward and grow match by match," Inzaghi commented.
"We are full of it up front and I put four attackers on the pitch, thinking that it would help us draw the match. You put the quality where you have it.
"We have to improve because I know where we started from. I thought that we were further behind Juventus but instead we are a lot nearer to them than I imagined."
Juve defender Leonardo Bonucci also feels Milan are on the right path, after a disappointing season last time out that saw Allegri and Clarence Seedorf both at the helm.
Bonucci believes Milan can enjoy a more promising campaign but feels a visit from the champions - who have won Serie A in each of the last three seasons - was simply too big an ask for Inzaghi's side.
"It's hard to get going again after a season like they had last year, especially if you're up against a team that's dominated the previous campaigns," the Italy international told Juve's official website.
"Unfortunately for them they ran into a strong, mature Juve side that's used to playing this sort of contest."