Holland international Van Persie has finalised a ?24million switch to Old Trafford, having earlier in the summer announced he would not be signing a new deal with the Gunners.
"The reality is when the player doesn't want to stay you have two ways: you either force him to stay or you accept the reality and you let him go. I have chosen the second solution," said Wenger. "I know it is a massive challenge and a massive gamble I took."
He added: "We have the quality to deal with the problem we have, and at the end of the day I can talk and talk and talk but we can only show it on the pitch now."
Van Persie is the latest of Wenger's key men to move on following last summer's departures of Cesc Fabregas and Samir Nasri - with Alex Song the next possible transfer amid reports of a £15million bid from Barcelona.
While the manner of Van Persie's exit may not sit well with many Arsenal fans - following his carefully worded summer statement questioning the direction of the club which stood by him during injury-plagued spells on the sidelines - Wenger maintains it is now time for everyone to look to the future as he prepares for Saturday's season opener against Sunderland.
He added: "Time heals all things and of course at the moment people are hurt, which I understand, but what is important for us is to focus on the season in front of us. Players have gone, life goes on and the football club is 125 years old and other big players have left this club and we have always gone from season to season in a strong way."
While Wenger may not want to go on the record over his personal thought on the saga, there remains a sense of having been let down by the Dutchman, whom he brought to Arsenal as a raw talent in May 2004.
Publicly, though, the Gunners boss maintains people should remember what Van Persie contributed on the pitch, plundering 30 league goals last season to fire them into third place.
"We lose a great player, a world-class player, I don't deny that, it is a massive challenge to replace him, so we have to be even more of a team and work even more together to compensate that loss," he said. "However, we have lost world-class players before and we always survived."
Source: PA
Source: PA