The Italian giants appeared to be cruising to a comfortable victory taking a 2-0 lead through Lucio and Giampaolo Pazzini.
But the Russian side staged a comeback to level the score at 2-2 before Mauro Zárate scored the winner for Inter 12 minutes from time.
Speaking after the match, Ranieri, who has now won his first two games since being appointed Inter coach, hailed his team's efforts but warned against complacency.
"I'm happy for two reasons: for the way we played in the first half, and for our pride in the second. It was the same against Bologna [FC on Saturday] when they equalised, because my players immediately tried to hit back and we managed to win the game," he was quoted as saying in UEFA.com.
"We cannot get too carried away, even if this team is packed full of great players. Many of them are injured but we will soon have them back, and those who are playing now are giving everything.
"It's a good sign, it's exactly what I want from my players right now - pride and determination to show that this team is not finished. "
The Italian coach went on to play down his impact at the club and revealed his hopes for Inter both domestically and in Europe.
"I'm sure, with a bit of luck, that we can have a say both in Italy and in Europe. [Gian Piero] Gasperini did not have enough time and enough luck; it's not easy to deal with so many injuries after all. For my part, I merely field players where they are used to playing and it worked well today."
Inter are currently second in Group B behind surprise leaders Trabzonspor.