The Argentine midfielder dedicated his strike against the Turkish side to his family, which helped to confirm the Italians as group winners
The 23-year-old, who joined Inter from Velez Sarsfield in the summer of 2011, gave the Serie A outfit the lead after 18 minutes of play following a one-two with Diego Milito, and Alvarez dedicated the strike to his family.
"This was a night to remember – scoring my very first goal for Inter. To do that at Champions League level makes it even more special," Alvarez told Uefa.com.
"After I scored, I ran towards the camera to dedicate my goal to my relatives in Argentina. I left my home country to try my luck at Inter this summer, and for a young player like me that is quite a big step. Without my family's support I would never have had the courage to do so."
Alvarez, who made his 10th appearance for Inter on Tuesday, has a contract at San Siro until the summer of 2016.