After winning a string of titles under Roberto Mancini and Jose Mourinho, the Nerazzurri have been shut out in successive seasons.
And what makes this year's setback even worse is that the club will not compete in the Champions League in the 2012-13.
"We need to reflect on our campaign and understand where we have to improve," said Inter coach Andrea Stramaccioni, who replaced Claudio Ranieri in March following his dismissal by the club.
"We are not satisfied with finishing sixth and we must improve."
The Nerazzurri lost 3-1 at Lazio last night to suffer their 14th defeat in Serie A and finish 26 points adrift of Italian champions Juventus.
Inter have at least secured a place in the preliminary round of the Europa League.
"Now we must prepare for an early start to the campaign," Stramaccioni said.
"We have managed to take a European spot after a difficult campaign and there is a great will to bounce back from a season like this one because a team and a club like this one deserve better.
"We are already working with the president and the club executives to construct a competitive team that can be at the level of our history."
Inter president Massimo Moratti has yet to confirm if Stramaccioni will coach the team next season.
"With regards to whether I will stay in charge, that is something that you have to ask Moratti," Stramaccioni said.
"He decides when to make the announcements."