"We stayed calm and didn't give any opportunities to Milan, and I think in the end they were lucky we didn't score even more," he said.
AC Milan coach Carlo Ancelotti admitted they had played badly, but promised a reinvigorated approach to the competition once key players return from injury.
"We'll now wait to see what the draw gives us and, in February, we will welcome back a few key players who have been injured," he said.
AC Milan, like the other group winners, will have the advantage of an away tie first in the next round while two-time winners Inter Milan, who finished second in Group B behind Bayern Munich, will play at home first.
Roma, like Lille, joined the last 16 for the first time when they beat Valencia 1-0 on Tuesday to finish second in Group D.
Arsenal manager Arsene Wenger, who has just celebrated 10 years working with the Gunners, joined his old foe, Ferguson, in applauding the influence of the Premiership on the competition.
"That shows how much the Premiership has improved," Wenger told Sky Sports.
Arsenal, who are only just getting over their defeat in last year's final, could face Barcelona in the next round, in a rematch of last year's final.
The other clubs to qualify were 1988 winners PSV Eindhoven, four-time winners Bayern Munich and two-time winners FC Porto.
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