The 21-year-old, who signed for the Merseyside club from Roma last month, scored his first goal for the Reds during Liverpool's 3-0 win over FC Gomel in the second leg of the Europa League third-round qualifier.
"It was absolutely a day to remember," Borini told the club's official website. "The fans were amazing and the atmosphere was unbelievable, just for a Europa League qualifier. To also get a goal was amazing.
"It felt like it was the first goal I had scored in my entire career. I tried to celebrate as I did for my first goal in Serie A."