The opening day loss at home to Villa resulted in supporters questioning Arsene Wenger's status as manager, expressing their unhappiness at the Gunners' lack of progress in the transfer market.
However, a 3-0 victory in the Champions League at Fenerbahce quietened the dissenters in midweek and first-half strikes from Olivier Giroud and Lukas Podolski (two) today lifted the mood further.
On-loan Aston Villa striker Darren Bent netted on his first Fulham appearance in reply, but the match was already lost by then and Ramsey was happy to come away from Craven Cottage with the points in the bag.
"We picked up where we left off in midweek," the Welshman told BT Sport.
"We had a great performance in Fenerbahce and we wanted to carry that on.
"After the disappointment against Villa it was vital to get the win today and we did it. They were a good team, they pressed us early on, which we had to adapt to, but we managed to get through that and played very well today.
"It's always difficult to come here, it's a tight pitch and the crowd are right behind them and they're a physical team, well organised and hard to break down.
"In the first 20 mins they closed us down pretty quickly and we had to deal with that and move the ball a bit quicker, and we got through the game in the end."
Wenger was also relieved to get their campaign off the ground and was more than happy with the performance his players put up.
He said: "It's never easy to play way or win away and we did it in a convincing way.
"In this kind of game it's important to be 1-0 up because they make things difficult for us and try to catch us on the break, so I thought we controlled the game well.
"We had a disappointing result against Villa and it was important to respond, and we've had two convincing wins first against Fenerbahce and again today here."
The Gunners have another tricky week ahead with the return match against the Turkish club before the prospect of a north London derby against Tottenham.
However, Wenger is refusing to look beyond their European match, saying: "We have a big game now on Tuesday night to get into the group stage of the Champions League.
"After that we'll think about the rest."