Inter goalkeeper Julio Cesar was the difference between the two teams and said at the final whistle: "I am happy because I was able to help the team on a very special day.
"We did not play our best football, but it was important to get back to a victory."
Inter now face Liverpool in the return-leg of their Champions League clash and Julio Cesar added: "We know it won't be easy and that we will have to run ourselves ragged. Our fans have sold out San Siro and have so much faith in us.
"We too are aware of our strength and will play the game to win, then we'll see what happens."