The under-pressure coach criticised his side's poor passing but claimed the Rossoneri deserved a point from their performance against the Costa del Sol outfit
Manuel Pellegrini's side won their third Champions League game in a row to take charge of Group C with Allegri's charges left five points further back in second.
The 45-year-old Italian suggested wasteful posession had undermined his side's chances of getting a point he felt they otherwise deserved.
"We threw the ball away a little bit too much when we were attacking," Allegri told reporters.
"We should have kept it more [but] a draw would have been the right result.
"Malaga did not surprise me. They have good players, with good technique."
The defeat leaves Milan's chances of progress in the balance and Allegri fighting for his future at San Siro following a poor start to the domestic season.
However, the Rossoneri coach doesn't seem to be too worried about his future for now.
"There is little to talk about, we just have to keep looking for a win," the former Cagliari boss claimed when asked if he still had the support of vice-president Adriano Galliani.
"I feel the trust of my players and in the league we will certainly improve our situation. In the Champions League we are still in a good position to qualify.
"Certainly we can say we have not been lucky in this recent period as we have missed good chances and we are punished for every mistake we make. We will now have to turn our attention to the next game."
Milan resume match action on Saturday when they host Genoa.