Walter Mazzarri's side crashed out of the Coppa Italia with a 1-0 defeat at Udinese on Thursday, all but ending their hopes of winning a trophy this season.
The Milan outfit were also beaten by the same scoreline at Lazio in Serie A on Monday night and have now won only two of their last eight games in all competitions.
The coach said: "This year we have eight players with expiring contracts, which says a lot about the rejuvenation project.
"They got me from Napoli because they know what I did there, taking a team from the bottom of the standings to seventh place.
"And you all know how it went from there. We expect to climb as high as we can doing what we're doing."
He added: "Qualifying for the Europa League? I don't place limits for myself, and people who know me know that.
"I send the players out there with the desire to win everything. Napoli set out every season without making many proclamations, then ended up qualifying for Europe each time. That could easily happen here too."
One positive to take out of Inter's cup defeat was that striker Diego Milito came through his first 90 minutes of the season after recovering from knee and thigh injuries.
Eugenio Corini's side are two points above the relegation zone and were hammered 4-1 at Torino in their last Serie A away game.
