Arsene Wenger's men got off to a fine start as they went in search of their first top-flight title since 2004, and were top for more than 100 days.
They fell away in the second half of the season, however, and suffered heavy defeats at championship rivals Manchester City, Liverpool and Chelsea.
Ramsey, who scored the winning goal in the 3-2 victory over Hull City in the FA Cup final to end the club's nine-year trophy drought, pinpointed those below-par defensive displays as defining factors in their failing title challenge.
"We got off to a really good start, that's something we had been lacking over the last few years," he told the club's official website.
"We came out of the blocks firing and were top of the league for long periods of the season.
"Everyone was really excited and looking forward to it, thinking that we've got a great opportunity. Unfortunately it wasn't to be.
"I think the results away from home against the so-called bigger teams have been damaging and that's what's cost us in the end.
"In all of those games we conceded early on and going to these places is difficult, never mind going a goal down. I think it's important just to stay in the game and frustrate them.
"With the quality we have, we always know we can create opportunities. The main thing is just to stay in the game in the first half and it will open up a lot more in the second half - and hopefully we can take full advantage."
