Fati, 17, became the youngest goalscorer in the Champions League with his effort at the San Siro.
" They've just told me," Fati told Barça TV after the game when asked if he knew he'd broken the record. "I am super happy with the goal and with the team's win.
"It's a dream, everything seems to be going really quickly, now it's just about enjoying myself and learning from the best."
He added that the silence around the San Siro when he scored stood out.
"I give it to Suarez and he gives it back," he said. "And when I score I was surprised because the whole stadium was silent. I was thinking: 'What have I just done?'. But I am really happy.
"Every time I get a chance, I will try to take it, with goals or, at least, by working hard."