The tactician was thrilled to see his side overturn a deficit and proceed to lift the trophy, as he emphasised their character and dismissed talk of reinforcements
The Serie A champions were on the back foot for most part of the match after Wesley Sneijder put the Coppa Italia holders in front midway through the first-half, but goals in quick succession from Kevin-Prince Boateng and Zlatan Ibrahimovic after the hour mark ensured the red half of Milan would bask in Super Cup glory, much to the relief of Allegri.
"It was a difficult game, and a difficult game to start the season with, it was not easy," admitted Allegri, according to Calciomercato.
"We did not start well but we never gave up. We grew in stature and then rewarded our hard work with two goals.
"It was a great victory and we must show the same spirit from the second-half for the rest of the season."
The 43-year-old was then quizzed on possible new arrivals before the end of August, but unsurprisingly, the coach was in no mood to discuss their transfer plans.
Indeed, Allegri wanted the occasion to be dedicated to their Supercoppa winners on the field, adding: "Reinforcements? Right now I'm happy with the guys at my disposal, because they are all great players with great personality."
Milan will now proceed to prepare for their Serie A opener on August 27, with an away trip to Allegri's former side Cagliari.