Gus Poyet's men are still involved in the FA Cup and visit Hull City in the quarter-finals this Sunday, handing Sunderland a chance to put the disappointment of Sunday's defeat to City behind them.
Victory at the KC Stadium would see Sunderland head back to the national stadium in the last four, a prospect that Borini is relishing.
"I want to go back there, to be at Wembley," Borini is quoted as saying by the Sunderland Echo. "Scoring at Wembley is always special, especially for a foreign player.
"If we can win against Hull, we'll be going back again, which will be good. But the main thing is to get points and start pushing up the league.
"We've seen what it's all about and hopefully we can push on now in the league."
Yaya Toure, Samir Nasri and Jesus Navas found the net after Borini had given Sunderland the lead in Sunday's final, but the Italian forward - on loan from Liverpool - feels there are plenty of positives to take from the performance.
"The only negative is the result," he added. "We were disappointed, but proud of what we did on the pitch.
"We made Man City win the game and they had to score two incredible goals, which is why they are Man City.
"It was a great team performance in the first half.
"Man City came out with the qualities, that's normal. But the feeling to be in front and have a real chance to win it was unbelievable.
"That's what we need to take with us for the rest of the season."
Sunderland currently sit one point adrift of safety in the Premier League, with a game in hand over 17th-placed West Brom.
