The Gunners were top of the table at the turn of the year but have fallen off the pace, although they are still favourites to finish in the top four ahead of Everton.
Ramsey scored his first goal since returning from a four-month injury layoff in the 3-0 victory over Hull City last weekend, which lifted Arsenal one point above the Toffees, and has stressed that playing Champions League football remains the priority at the club.
"We are hungrier than ever to get this, the Champions League, to get into that again - this is where we want to be," the Wales international told Sky Sports News.
"That is where the players want to play and test themselves and that is no different this season, to finish the job off and get back in for next season."
Ramsey has scored eight goals in 18 Premier League starts this season.