The 30-year-old netted both goals as the reigning champions overcame Wigan at Wembley on Sunday to lift the Community Shield in David Moyes's first official game in charge.
But United have had mixed results during their pre-season programme and are yet to make an impact in the summer transfer window, with bookmakers naming them third favourites for the title behind neighbours Manchester City and Jose Mourinho's Chelsea.
Van Persie does not want to acknowledge those odds, though, as he is confident that the current team can repeat last season's runaway success to retain their Premier League crown.
|5/2||Manchester United are 5/2 with Bet365 to win the Premier League
"We've got [Wilfried] Zaha who has done really well and, as I said earlier, I believe in this team.
"I don't want to be funny but we are the champions. So third favourites? Can you explain that? I don't really care. I believe in this team and I believe that we will compete until the end again."
Ryan Giggs was impressed with Van Persie's performance against the FA Cup winners and hopes the striker can reproduce his 26 goals to fire United to the title again.
"The first goal was a brilliant goal and the timing was brilliant," the veteran added. "It was a great start for us, we hope Robin can reproduce the form he showed for us last year.
"We just know we've got good players in the team. It's always hard when you’re champions, you've got to reproduce the form you showed last year and I hope we do that."