Toro won 2-1, with former Southampton striker Che Adams scoring on debut.
Vanoli later said: “I congratulate my lads, they’re put in an important shift, which backs up our performance against Milan.
"It’s August and we dropped off a bit in San Siro, but now we have put more fuel in the tank and we have added another piece to our footballing puzzle.”
On Adams, he added: “We took him because he’s a great player, like all our other strikers.
"(Antonio) Sanabria did well in Milan, I like playing with two strikers.”