Last season's Premier League top scorer signed a four-year deal at Old Trafford, ending an eight-year stay with Arsenal for whom he scored 132 goals in 278 appearances.
"We regret that we have lost a great player and for one simple reason - he only had one year left on his contract. He wanted to go," Wenger told a news conference on Friday.
"We anticipated this situation might happen, therefore we bought Lukas Podolski and Olivier Giroud.
"[Selling to a rival] is not what we wanted but there was not much choice. We had only one club really interested at the level we thought would be acceptable and that was Manchester United.
"At the end of the day, was the only decision we could make."
British media reported the deal to be worth £24 million and Wenger said Arsenal had already "invested the money" with the signings of Spain international midfielder Santi Cazorla from Malaga, German international winger Podolski from Cologne and France striker Giroud from Ligue 1 champions Montpellier.
"If needed we will invest more, but if you look at the number of players we have, we have a massive squad. We have plenty of players who have no chance to play at all.
"At the moment I believe we have what is needed to be ambitious and to play our game."
Arsenal, third in the league last season - 19 points behind the Manchester clubs - begin their campaign with a home clash against Sunderland on Saturday.
Winger Alex Oxlade-Chamberlain (ankle) and defender Laurent Koscielny (calf) miss the game through injury, but forward Theo Walcott, who pulled out of England's friendly with Italy in midweek because of a bruised thigh, has recovered.
Defender Thomas Vermaelen will replace Van Persie as Arsenal captain.
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