Iachini's Palermo had lost three of four fixtures on the road in 2014-15 prior to their trip to the San Siro but they produced an impressive performance to upstage Milan 2-0.
Milan defender Cristian Zapata gifted Palermo a 23rd-minute lead, heading beyond goalkeeper Diego Lopez.
And Zapata was at fault for Palermo's second goal three minutes later, easily brushed aside by Paula Dybala as the Argentinean striker found the back of the net.
The two first-half goals were enough for 13th-placed Palermo to claim their first away triumph of the 2014-15 campaign.
"We continued to play and believe in what we've been doing for over a year with this squad," Iachini told Sky Sport Italia.
"At times we've done equally well against big teams without getting the result we deserved.
"This is satisfying for the lads and the fans but we haven't really achieved anything yet and have to keep pushing.
"We need to put into practice what we test out during the week. Over the weeks we have grown in confidence and now we are reaping the rewards.
"Milan are an excellent squad and seeing what they did in previous rounds, we knew that we needed a perfect Palermo performance.
"By moving the ball around quickly and pressing them high up the field, that was the only way to really hurt them."
