The hosts were stunned by a last-gasp Alberto Gilardino goal as they fell to a potentially costly defeat against Champions League qualification rivals Milan.
"There's a lot of bitterness, especially as the same thing happened against Empoli when a good result became a bad one in the last few minutes," Handanovic explained.
"We lost precious points and we deserved to win as much as they did. We played excellently, but we have to accept the verdict on the pitch.
"Now we have to look forward and luckily there isn't much time to think because we are back on the field for the Coppa Italia on Wednesday."