Monday's victory over Newcastle means Arsenal now need one win from their remaining two games to guarantee Champions League football for a 17th straight year.
A crack at the title appeared possible when Arsenal led the table at the turn of the year, but Ramsey, Mesut Ozil, Theo Walcott and Jack Wilshere have all missed significant periods since then.
And, according to Arsene Wenger, those absences go some way to explaining heavy away defeats against Liverpool, Chelsea and Everton in the space of two months.
Ramsey told Sky Sports News: "We've had a lot of injuries to key players at the same time which did affect us, but that's football. Things happen like that.
"Obviously you do have thoughts going through your mind about what could have been.
"The only games that have let us down this year are against the top-five away from home: if we'd managed to nick a couple of results against Manchester City, Liverpool, Everton and Chelsea the gap would have been a lot smaller and we'd have been right there.
"That'll be something to improve on next season - we'll need to be more streetwise in those games."
Victory over Hull in next month's FA Cup final would mean going into next season without the pressure of ending a nine-year trophy drought.
Ramsey said: "We're hungrier than ever to win this trophy, and hopefully that'll be the trophy to kick off very successful seasons in the near future."
Arsenal can clinch Champions League qualification if they beat West Brom on Super Sunday. Watch the game live on Sky Sports 1 from 1.30pm