The experienced coach lamented his side's lack of luck in the tie and declared that the Nerazzurri deserved to go through in the competition
The Italian giants secured a 2-1 victory at San Siro in the second leg of their last 16 tie with goals from Diego Milito and Giampaolo Pazzini, but still crashed out of the competition with a 2-2 aggregate scoreline on the away goals rule.
"Perhaps we played better in the first leg, but I would say that we had the best chances of the tie," Ranieri told Sky Sport Italia.
"Suffering a goal at the end is surely hard to digest. This match was a snapshot of our season.
"We could not have done more than we did here."
Milito's goal 15 minutes before the end of the match seemed to take the match to extra-time, but an injury-time goal from substitute Brandao put the game beyond the Nerazzurri.
"In the second half, I asked [Wesley] Sneijder to act more like a playmaker, but then he got injured," Ranieri continued.
"When Obi came on, we got stronger. Overall, I think that our elimination is unfair.
"I thought that we had turned the tide after the match against Chievo, but I was wrong.
"Tonight the thing we lacked the most was luck."
This latest setback will put Ranieri under even more pressure, but the 60-year-old believes that Inter still have plenty to fight for before the end of the season.
"Our motivations? We will find them in ourselves," Ranieri noted. "This team has given everything and that is how it will continue.
"We still believe we can finish third in Serie A, but things must improve."