The Black Cats were on course to cause an upset on Sunday thanks to an early Fabio Borini strike, but two goals in as many minutes from Yaya Toure and Samir Nasri turned the game 10 minutes after the break before Jesus Navas added the third in the dying seconds.
Manager Gus Poyet told his players after the match that a similar display to the first half at Wembley will give the team an excellent chance of retaining their Premier League status.
Asked about the manager's comments, Brown said: "He just said, 'listen, we have got important games coming up now and if we can play like that in the first half, we can play like that every week'.
"We have just got to take that in and make sure we do it in the league now.
"They scored two fantastic goals and managed to kill us with a third, so it was disappointing.
"But the lads can keep their heads up high and we have to start taking that sort of form we had in the first half into the league now.
"We can do it against the big teams, so we have just got to keep it going against the teams around us now."