Inter took control of the round 16 tie with the 1-0 first-leg triumph.
Arnautovic said: It is certainly one of the most important goals of my career.
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This was not an easy time for me after the injury, I took a while to get back and in recent weeks I had a lot of chances where I didn't score, and scoring goals is what I am here for.
So when I had those two chances and didn't score this evening, goals I ought to score. But the fans and the players all showed they are behind me. That was an incredible moment for me, it gave me the energy I needed to score the goal."
He added: I think we are a fantastic group. Those who start regularly or who are on the bench, they all feel the same. Those on the bench do not let their heads drop, they come on and do what they need to do in order to win the game."