Stefano Pioli was delighted to end a difficult week for Milan with what he felt was a deserved win over Bologna - but opposite number Sinisa Mihajlovic begged to differ.
The Rossoneri went into Saturday's game off the back of two successive defeats. After going down 3-0 at home to Atalanta in Serie A, they were knocked out of the Coppa Italia in midweek by rivals Inter.
Having been sent off against Inter and forced to deny suggestions he made a racist comment towards Romelu Lukaku during the quarter-final tie, Zlatan Ibrahimovic missed a penalty as he failed to reach 500 goals in his club career.
However, Ante Rebic tucked home the rebound to give Milan a half-time lead and Franck Kessie made no mistake from the spot in the second half.
Substitute Andrea Poli halved the deficit in the 81st minute but Bologna were unable to find an equaliser, Milan becoming just the third team to win nine of their first 10 Serie A away matches in a season.
"Without committing the naive error for the Bologna goal, we had an excellent match," Pioli told Milan TV.
"I'm happy with the performance and it's a victory which gives us confidence at the end a difficult week. It's deserved.
"The last two training sessions we've done this week are the best in a long time. We have seen the return of important players and the team has managed to maintain a balanced attitude.
"We were not happy with the performance against Atalanta, the only team that has put us in difficulty this season. We played it out against all the others."
However, Mihajlovic felt Bologna were the better team in open play, insisting that Ibrahimovic's presence in his line-up would have led to a comfortable home victory.
"We created three or four chances and didn't score. It was an undeserved defeat and I think we played better," Mihajlovic told Sky Sport Italia.
"Fine, Milan are a better team, but we created our chances from open play. They scored from penalties and their only chances were from long balls.
"If we had Ibrahimovic on our side, we would have won 3-0. My players should be proud of their performance, they fought to the end, but as usual against bigger teams, we play well and don't win."
As well as the penalty, Ibrahimovic was also denied by a fabulous double save by Bologna goalkeeper Lukasz Skorupski in the first half.
The talismanic striker was on target with three of his four attempts in total but will have to wait to reach the personal milestone. He has now missed three of his six penalties taken in Serie A this term, one more than in his previous 17 spot-kick attempts for Milan in the top flight.
Ibrahimovic will hope to make it to 500 goals when the league leaders host struggling Crotone at San Siro next weekend.