The Welshman, who scored 16 goals last season despite suffering from injury problems, said his team need to stop conceding so many goals against their major rivals if they are to improve on their fourth-place finish.
Arsenal took five points from six games against the three sides who finished above them and suffered heavy away defeats to Manchester City (6-3), Liverpool (5-1) and Chelsea (6-0).
"I think there's going to be about six teams involved right until the wire (in the title race this year)," the 23-year-old told the club's website (www.arsenal.com) on Thursday.
"It's important in those games [against the top teams], especially in the first half. These places are difficult enough to go to and get results, especially when it's 0-0, never mind when it's two, three or four-nil down in the first 25 minutes.
"We're going to have to be a lot more streetwise when going to these places and maybe we'll have to sit back in the first half and then the game will open up in the second half and we know we'll create opportunities.
"It's going to be difficult but I think we have a great team here and great team spirit. We're in a good place at the moment.
"Hopefully, we can get off to a good start in the season and put (ourselves) in a good position and hopefully last season where we fell away a bit we'll improve and put that right. [If we do], we'll have a great opportunity."
The Premier League season starts on Saturday, with Arsenal hosting fellow-London club Crystal Palace.
Arsene Wenger's side ended their nine-year wait for a trophy when Ramsey's extra-time goal in the FA Cup final secured a 3-2 win over Hull City in May.
They followed up with more silverware on Sunday after a dominant 3-0 win against league champions Manchester City in the Community Shield, their first victory in the curtain-raiser for the new English season since 2004.
Ramsey, who scored in that victory, believes that Wenger doing early business in the transfer market with the signings of Alexis Sanchez, Mathieu Debuchy and Calum Chambers has been good for the squad, ensuring they are ready for the new season.
"Over the last few seasons we have (sold) some of our bigger players but the squad is really settled now and we've done the business early this year," Ramsey added.
"That's helped us to get used to some of the players before the season starts. We've brought in some big, quality names as well so I think that we've done well and we're all looking forward to teaming up together."