Barca endured a real tussle with Inter at San Siro, only securing a late win thanks to Fati's 86th-minute strike.
That goal made the 17-year-old the youngest scorer in Champions League history and sealed Inter's fate, as the Serie A side drop down to the Europa League after finishing third in the group.
Perez had opened the scoring with a composed finish, and his thoughts quickly turned to Barca's La Masia after the match, with the famed academy receiving criticism in recent years for a perceived lack of homegrown players reaching the first team.
"It is something incredible that we are both living," Perez told Movistar. "Both Ansu and I are an example for La Masia if you think you can get there [to the first team].
"Barca trust the people of academy and that is the most important thing."
Barcelona's 17-year-old Ansu Fati waves goodbye to Inter's Champions League season ✨ pic.twitter.com/joLITbWZJx— Bleacher Report Live (@brlive) December 10, 2019
Coach Ernesto Valverde also spoke of the two goal-scorers and was particularly thrilled by Fati's record.
"Carles has the nose for more goals and strikes the ball really nicely," he said. "Ansu is a born scorer and, although he's had some niggling pain, we wanted him to have some minutes.
"That it's a Barca lad who's the youngest ever scorer in this competition delights us."
Barca had already secured top spot in the group and will find out their next opponents in the Champions League during Monday's draw.
The Catalans face Real Sociedad at the weekend before then going head-to-head with bitter rivals Real Madrid in El Clasico on December 18.