The struggling home side got a huge slice of fortune when defender Cristian Zapata's drive in the 82nd minute appeared to be heading wide before it deflected off Parkhead left-back Emilio Izaguirre and ended up behind Fraser Forster.
The Hoops boss, who guided the Scottish champions to a last-16 spot last season, said: "I am bitterly disappointed because for long periods of the game we were the better team.
"To come away from the San Siro, (disappointed) not to have picked up a point or three points, is a mark of how well we have developed and how well we played tonight.
"We have Barcelona next and they are a different animal. But we are here to qualify and nothing changes my view after that performance.
"You have to take the chances when you are on top but unfortunately we didn't get the break of the ball and they did with the deflection with the first goal.
"But I think the scoreline flattered Milan, I don't think there was two goals between the teams.
"We dominated from 20 minutes on in the first-half, until 10 minutes from end of second-half.
"Apart from the Muntari chance, my goalkeeper had nothing to do the second-half, we restricted them to long-range shots and we played really good football.
"There was no failures. We didn't hang on, there wasn't wave after wave of attacks, we took the game to Milan and we surprised a lot of people tonight.
"I thought we were the better team playing the better football.
"We had really good chances tonight and that will be one regret going away from here."
Milan play Ajax in their next fixture and head coach Massimiliano Allegri will be hoping his lengthy injury-list which included Kaka and captain Riccardo Montolivo, will have shortened substantially.
The Italian side looked looked disjointed for most of the match and will have to improve considerably if they are to reach the knockout stages from which Allegri is not discounting the Scottish champions.
He said: "We had luck a couple of times in the game tonight but it was a positive performance and an important victory for us.
"Celtic are a very good team. I believe they still have chances of qualifying out of the group but everything is still open so we will see.
"My side improved in the second part of the game and they will improve further.
"There are some players who haven't played before but this team has to be admired, they all defend together."
- Sports & Recreation
- Cristian Zapata
- Mario Balotelli
- Sulley Muntari
- Emilio Izaguirre