"We started well, we got the couple of goals in the first half and showed tonight that we have plenty of characters in this team," Ramsey told BT Sport after the game.
"It's never easy to come to the San Siro and play AC Milan. I know that from past experience when we lost 4-0, so I'm really pleased we came here and got the win."
"We played really well in the first half and created many opportunities. We wanted to protect it in second half and all in all, it was a good night's work.
"It's up to us to keep focused and work hard. We know what we're capable of and we need to try to produce it more consistently. We've turned a little corner, and come here and got a good result."
Arsenal will now welcome Milan to the Emirates for the second leg on March 15.