The Wales midfielder scored the extra-time winner in last season's FA Cup final against Hull and hopes the Gunners can repeat the victory against Aston Villa at Wembley on Saturday before mounting a sustained Premier League title challenge next term.
Ramsey's winners' medal is in a trophy cabinet in his home "which is slowly growing," he said, as he targets another success after Arsenal's late-season charge secured third place in the league.
"Hopefully we can win the FA Cup this year
Then that'll be two things in two years so hopefully we can just keep that run of winning things going," Ramsey said.
"Back-to-back finals are not an easy thing to achieve
In the second half of the season we have shown the form that we need throughout the season to win this league.
"We certainly showed that we are capable of going on these big runs and not losing too many games.
"If we can just show that consistency throughout the season then we'll be challenging for the Premier League, and that's what we'll be looking to do next year."
Ramsey knows Arsenal must justify their position as favourites against Villa by going out to win the trophy.
"It's so important to have that hunger and determination to go out and prove that you're worthy winners," he said.
"It's not going to be an easy game, we're going to have to be aware of that, but all the lads are even more hungry to win something this time around.
"We want that feeling that we had last year and we want to go on and win more things."
Ramsey's strike against Hull completed a remarkable recovery from the Gunners, who fell 2-0 down within eight minutes.
"I was thankful in a way that they did score their two goals early on in the game and that we did have a large chunk of the game to get back into it," he said.
"That gave us the kick that we needed to get going
We managed to score before half-time and then it felt like we were in control of the game and created a few opportunities to get back into it.
"We managed to do that and to win in extra-time was amazing.
"To score a winner in the FA Cup final, it's everybody's dream and I managed to live it.
"To finally win something after all those years and the pressure that has been put on this club was such a nice feeling of relief to finally win something."
The 24-year-old hopes to experience the ecstasy of victory without the agony this season.
He said: "We never do it easy
We've experienced what it's like now, going a few goals behind early in the game, but we still believed in ourselves and our ability to get through it.
"Hopefully it will be a bit easier this time and we won't have to put so many people through that.
"Villa are a good team, very solid and of late they've been in really good form, so we'll have to be aware of that."
Ramsey is a rumoured target for Barcelona, once their transfer embargo is lifted, but he insisted he has one solitary focus.
"That's just something that's been written in the papers," he said.
"I'm focused on Arsenal and winning the FA Cup
That sort of news doesn't affect me or even enter my mind."
Source : PA