Barcelona boss Ernesto Valverde targeted Champions League glory after Inter Milan were dispatched 2-1 at the San Siro.
Carles Perez scored on his debut in the competition to seize the lead before Romelu Lukaku replied, but 17-year-old Ansu Fati struck the winner in the 87th minute, in the process becoming the tournament's youngest ever goalscorer.
"We feel obliged to win this competition. We want to win every single match and that's what we've achieved here," Valverde said in the post-match press conference.
"Carles has the nose for more goals and strikes the ball really nicely. Ansu is a born scorer and although he's had some niggling pain, we wanted him to have some minutes.
"That it's a Barça lad who's the youngest ever scorer in this competition delights us.
"We're thrilled because Inter are a really demanding rival. We played to win and my players, many of whom were making a debut of some kind, responded by showing competitive mettle."
Fati combined with fellow substitute Luis Suarez before drilling the ball home with a superb strike.
"I played the give and go with Luis and when I scored the stadium just went silent. I'm super-happy!" Fati said.
"It's a dream. Everything seems to be going at high speed. I just have to take every opportunity I'm given. But here, you look around and think: 'what have I done'?"
Defeat means Inter have failed to qualify for the round of 16 while Barcelona progress as group winners.
"Watching that Ansu Fati goal is painful, as it killed us in every way. We were pushing, creating the chances to score and go 2-1 up," Inter boss Antonio Conte said.
"I was also disappointed for the fans at San Siro, as they pushed us from start to finish and created a wonderful atmosphere. It should've ended differently.
"I think we deserved more in this group. Still I think it's all valuable experience. We have to raise our heads again."