The Croatia Under-19 international got the Nerrazzurri on level terms just before the stroke of half-time after Rubin went 1-0 up from the penalty spot.
But in the second half Inter fell behind again and had Japan international Yuto Nagatomo to thank for salvaging a draw at San Siro, Livaja says he could have been more prolific in front of goal.
Speaking shortly after the full-time whistle the former Hadjuk Split youth player told the club's official TV station: "I scored the first then I messed up the second... we didn't win but it was an enjoyable match.”
Livaja revealed it was exciting for him to open his account for the Serie A giants but at the same time remained level-headed about the moment.
He added: “Yes, it was an emotional occasion for me. I didn't go crazy after scoring. My aim is always to score goals.”
Although slightly disappointed with a home draw his focus has been immediately switched to this weekend’s Serie A clash with Siena. “Now we have to think about Siena, it's an important game,” he said.