Inter lead Group H following the 1-0 win over Partizan Belgrade on Thursday evening and the 36-year-old has talked up his team's chances of glory in the competition.
Stramaccioni said: "Inter care about this competition and it is our duty to be protagonists in Europe and Italy.
"We started in the preliminary rounds and want to go all the way. In the first half we suffered with the way they passed the ball around, I won't deny that.
"But we knew they were a very technical side. After the break it was an Inter monologue and we created so many scoring opportunities."
Stramaccioni replaced Claudio Ranieri at the San Siro.