Arsene Wenger's side were top of the league for a large part of the campaign, but defeats to fellow challengers Manchester City, Liverpool and Chelsea saw them lose ground and eventually finish fourth.
Arteta was particularly critical of their game against Chelsea, which they lost 6-0.
"It's been our fault – I can't find any other explanation. When you go to Chelsea and they score three amazing goals then ok, but we gave the ball away in our own half. They were putting pressure on us and we knew they would do that, but we kept making mistakes and in a big game your opponents won't miss their chance," Arteta told the club's official website.
"The games were over after 15 or 20 minutes, and that just can't happen. It's nothing to do with preparation – everyone is prepared, and when it happens once we expect that it won't repeat itself in the next big game.
"But it has still happened. Dropping points like that has been a big blow for everyone psychologically – it's been really hard to take. The goals we've conceded haven't been good enough from our point of view and we've paid for them, big time."
Despite their disappointment in the league, Arsenal won the FA Cup last week.