The victory for the Giallorossi came thanks to their Argentine contingent after goals from Nicolas Burdisso, Pablo Osvaldo and two from Erik Lamela put the home side in front before two late goals from Giampaolo Pazzini and Bojan Krkic brought some slight respectability to the scoreline.
"Milan are always Milan, so they are technically gifted and caused problems, especially when we went down to 10 men,” Zeman told Sky Sport Italia after the game.
"I am happy with the performance, especially the first half. In the second we tried to sit on our lead and we don’t know how to do that."
Zeman brought back midfielder Daniele De Rossi for the clash with Milan, and the move paid off as Roma bossed the midfield.
"It was a good game in the first half because we pressured them high up the field and were able to go on the counter," the coach continued.
"In the second half we got pinned back. De Rossi had a decent performance, although after the break he too struggled and was unable to catch his man.
"Pjanic is technically strong and does his job. I choose the line-up that gives me greater certainty to play good football.
"Bradley and De Rossi are more ‘breakers’ than Alessandro Florenzi, so I wanted to block Milan. In the second half we allowed Milan to play in midfield and it showed.
"If there were only 11 players in the squad, then it’d be easy. Seeing as there are 24, I try to use those who give me more guarantees for what they can do."
Roma’s Bosnia midfielder Miralem Pjanic backed up his manager’s comments by insisting that the victory means a lot to the players heading into the winter break.
"Tonight we were more than Milan," he said. "This means so much, in an important match against a good team.
"We played well, we were superior in all areas of the pitch and continue the streak."