Milan were made to work more than they expected after taking an early lead against short-handed Bologna on Saturday.
After taking a 2-0 lead at the interval with Bologna down to 10 men, the Rossoneri had a second-half scare at the Stadio Renato Dall'Ara before prevailing 4-2.
Stefano Pioli lamented his side's over-confidence heading into the break, with Milan fortunate to prevail after Ismael Bennacer and Zlatan Ibrahimovic netted late to secure the win.
"We struggled because we mistakenly thought that the match, with two goals and one more man, was over," Pioli told Sky Sport Italia.
"Fortunately we have the qualities to take it back and we won an important match. Even in numerical superiority we have lacked clarity, we were too frantic.
"With Ibra and [Olivier] Giroud ahead we made too many crosses, we had to play it more and move it more quickly. In the first 10 minutes of the second half we had to manage it better.
"It is a very important victory. We know very well that the matches after the European commitments are difficult."
Coming off a 1-0 Champions League defeat to Porto on Tuesday, Milan went top of the table in Serie A with Saturday's triumph.
Pioli said afterward that Ibrahimovic told him during the game he was "really tired" and indeed the talisman started the Bologna comeback with an own goal in the 49th minute.
Musa Barrow equalised three minutes later before Bologna's momentum was blunted when Robert Soriano was given a straight red card in the 58th minute, leaving the home side with just nine men.
Ibrahimovic played the full 90 minutes in starting his first league match of the season. His goal in the final minute capped the scoring.
"We are showing that we always believe in it, that we never give up," Pioli said. "It is clear that there is a bit of tiredness because there are so many players missing and we play so many games, but it is the mentality that makes the difference and we want to win games until the end."