The Gunners beat Aston Villa 4-0 in Sunday’s FA Cup final, sealing back-to-back triumphs in the tournament and becoming the most successful team in the competition's history with 12 wins to their name.
However, they finished 12 points behind league champions Chelsea, with Jose Mourinho’s side running away with the title after a strong start, the complete opposite to Arsene Wenger’s side’s poor opening eight games.
After an impressive 2015, though, Ramsey believes they can close the gap on their rivals next season with a title challenge.
“I think we are [closing the gap on Chelsea],” he said.
“I think we’ve learned in the big games how to manage them and it will be important to go into next season with that sort of mentality. The rest of the games take care of themselves.”
The Gunners can point to a number of things having cost them this season, with their early Champions League qualifier meaning they had to start sooner than everybody else, seriously hampering pre-season plans.
They also suffered a number of injuries over the course of the campaign, with the likes of Mesut Ozil, Mathieu Debuchy and several others having all spent prolonged periods on the treatment table at certain points.
Ramsey, though, feels that if they can keep everyone fit at the crucial moments next season, then they have a great chance of competing for the top-flight crown.
“As long as we keep players fit throughout the season and not lose players in vital parts, I think we will have a great chance,” he added.
“If we can get off to a good start — and we don’t have to qualify for the Champions League — we can focus on the League and go from there.”