Van Persie, 29, will complete his move to Old Trafford in the next 24 hours.
“It’s never great to lose players of that quality but he only had a year contract so we do not have a choice,” the Arsenal manager told French TV.
Arsenal legend Bob Wilson says striker Van Persie’s impending move to United has left him “bordering on anger”.
Wenger revealed he will not be replacing Van Persie – having already brought in Lukas Podolski, Olivier Giroud and Santi Cazorla this summer.
“We already recruited to replace him,” claimed Wenger on French TV station TF1. “We have already recruited since we bought Giroud and Podolski, who originally were intended to offset the departure of Van Persie.”
He added: “I’d have preferred to sell him abroad, to PSG [Paris St-Germain], for example, over Manchester United.”
Former Arsenal goalkeeper Wilson admitted his disappointment at Van Persie’s move to the Gunners’ rivals.
“I am disappointed, bordering on a little bit of anger almost, as Robin was made captain and did a fantastic job,” Wilson told BBC Radio 4.
“I read all his programme notes about the pride of being Arsenal captain, then a year later he leaves one great club for another great club.
“I’m taking the stance of the ‘the king is dead, long live the king’ – thank you Robin and goodbye.”
However, Wilson believes it makes good business sense for Wenger to let the Dutchman go.
“Obviously it is very good business from the Arsenal point of view. Their perspective is it is £24m for a 29-year-old who has a history of injury problems and one truly magnificent season in eight. That is great business,” said the former Arsenal player.
The ex-goalkeeper, who also worked at Arsenal as a coach, is still excited about the three new signings.
“I look at it and I’m very excited by the team Arsene Wenger is putting together,” said Wilson.
“The fact that Van Persie is gone is hugely disappointing, but he’s wiped out in one go a lot of the fee that was spent on three talented players – Podolski, Giroud and the Spaniard Cazorla.”
Belgium international Thomas Vermaelen is set to be made Arsenal captain following Van Persie’s departure.
“Any Belgian who captains a Dutch side in Ajax is a special player,” added Wilson.