The champions beat Wigan 2-0 at Wembley this to secure David Moyes' first trophy as a senior manager after a rocky pre-season campaign.
No major signings and speculation over the future of Wayne Rooney has led to an unsettled summer at Old Trafford but Van Persie is confident United will be in the hunt for silverware come the end of the season.
"We're doing really well and I believe in this team," he told ITV1.
"We are the champions and based on that we are clear favourites.
"I believe in this team and I believe that we will compete until the end again."
Over 80,000 fans flocked from Lancashire to London this afternoon and the Dutchman was pleased to get on the scoresheet via a spectacular header and a second-half deflection.
"It's always nice to score, especially at Wembley," he said.
"It's a great day for the fans, for us and for the manager as well. All of us.
"One day, one game and we've won a trophy so it's good. I'm really glad for everyone."
He added: "Last year I scored a couple of headers, not too many so I have to improve on that. I think it went in quite nice."