Milan have come under fire from their own fans of late for their poor domestic campaign, but the veteran stopper said that the win over the Scottish side was for their president and proves that the Rossoneri are still "alive and kicking".
"We want to dedicate this win to president Silvio Berlusconi," Abbiati told Sky Sport Italia.
"This was important for a series of reasons and in a very difficult arena we proved we're alive and kicking.
"Was it easier to play outside San Siro? I wouldn't say that, as you can really hear the Celtic fans singing! We closed up within ourselves and remained concentrated."
Milan will qualify to the knockout stages of the competition if they avoid defeat to Ajax in the next round of fixtures.