With City up 2-1 going into the second leg at Ashton Gate, Pep Guardiola's side survived a late scare to win 3-2 on the night and 5-3 on aggregate.
"We played a very good game, we are pleased," De Bruyne, who scored the winner in stoppage time.
"We didn't give them any opportunities, we should have won three or four nil. We came here, we knew the crowd would be up for it but we managed to keep them quiet.
"After we went 2-0 they played some long balls and got two goals but we deserved to go to Wembley. I was out with an injury last time so let's hope that we have the same result."