Tijjani Reijnders struck for Milan before Paulo Dybala scored an equaliser for the visitors.
Afterwards, Ranieri declared himself pleased with Roma's performance.
Is there any regret?
"What Milan did in the first half, we did in the second. We played a good game, satisfied with the performance. We came here to win and not have regrets if it had gone badly. We did our best and made some mistakes, but there is also the quality of Milan in the counterattacks, especially in the first half. Then we settled in better and it went as we wanted."
On substitutions for yellow cards:
"Having five substitutions... There weren't any before. When I played there were two. Now there are so many that it's right to take advantage of this opportunity. It was a fast and vibrant match. If I thought of substituting them and they got a red card it wouldn't have been good. Those who came on came on well."
If it's a team that is coming out of difficulty:
"Yes, the boys are fine and we are becoming a team. We are understanding the defects and how to fix them. We are working well."
On Dybala reborn:
"I didn't release him. You give too much credit to the coaches. They are players who do this if they are well. He hasn't had any problems for a while."
If the derby comes at the right time:
"I say this after the match. We are doing well, they are in a fantastic moment. Congratulations because they are playing well and are where they are because they deserve it. The derbies are games apart."
On open doors training:
"The fans are great and I hope they are proud of how the team played and fought, looking for the full result. He didn't come, it was written that way. Sooner or later we will win away from home. We opened up because they told me there was a chance to wish the fans a happy new year. It seemed like the right time, given that the schools are closed and the children can come."