Gabriel Jesus scored the only goal of the game in the fourth minute, to ensure City booked another date at Wembley for the final.
Sterling was a constant threat on the flanks and almost got his name on the scoresheet in the second period, but he was denied by a good save from Matt Ryan.
And reflecting on the hard-fought win, Sterling said: “Brighton played brilliantly, and they caused us problems from set-pieces. They stayed in the game for long periods, but we showed the spirit that we have to hold on.
“It was a difficult game for us, but we managed to get through it. There are still some huge games coming up for us and we’re already looking forward to Tuesday (the Champions League quarter-final first leg tie away at Spurs).
"Our focus is now solely on that.”
The England star received widespread praise prior to the game for his wonderful gesture in handing out 500 free tickets to students from his old school, Ark Elvin Academy, formerly known as Copeland Community School when Raheem attended.
And the winger said he was delighted to be able to give the youngsters such an experience.
He added: “When I was growing up in the Wembley area, sometimes I could only watch the games on TV.
“Lots of kids don’t get the opportunity to step foot inside this stadium. The most important thing for me was to let them experience a day like this."