Alexandre Lacazette struck late on for the three points.
Ramsey said, "We wanted to take full advantage against the opposition today. We had a difficult start losing to Manchester City and Chelsea but we have bounced back. We know going to be difficult here, the crowd is superb, so if you give them any chance you can really feel the atmosphere, so we did well to overcome this."
On playing in Cardiff, he added: "It is always emotional, I love coming back to play here in front of these fans. It is where I was brought up and given opportunity to play football so I will always be grateful."
And Ramsey says the win showed the players are adapting to manager Unai Emery's demands.
"We know it is a process and every game we improve that little bit and get stronger and stronger. Hopefully can come back from International break and really kick on."