Ramsey and Henrikh Mkhitaryan struck for the 2-0 first-leg win.
Ramsey said: “We started well, we got a couple of goals in the first half and we have shown we have plenty of character in the team.
“It is never easy to come to the San Siro and play AC Milan, we came here before and lost 4-0.
“We played well in the first half and moved the ball well and kept a clean sheet.
“We have been on a bad run, but sometimes you train hard and it does not work, but we know what we are capable of."