Filippo Inzaghi's future as Milan head coach is sure to come under further scrutiny as his side failed to turn their dominance of possession into a sustained attacking threat - Keisuke Honda's second-half effort that rattled the crossbar proving their best chance.
A draw leaves Milan some 11 points off the UEFA Champions League places in Serie A, while the gap to guaranteed Europa League football is five.
Bocchetti insists that a return to Europe remains Milan's top priority, but concedes the team must do more to take advantage of their opportunities.
"I am happy that the defence didn't concede a goal. We had three or four opportunities that we could have dealt with better," he told Milan's official website.
"We must all give that little bit extra because our objective remains European qualification.
"We have to give more starting next Saturday against Hellas Verona and win."
Team-mate Luca Antonelli echoed Bocchetti's sentiments, adding: "The only positive note is that we kept a second successive clean sheet.
"We were the only side to attack in the first half, in the second we had two chances, and Honda hit the bar.
"Our objective is to qualify for Europe, we will try and give something extra to achieve that. I am sorry that we weren't able to pick up three points for the fans."
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