"We always worry about the young talent coming through, and obviously seeing Danny leave Manchester United is sad," he told the BBC.
"But the manager knows what he is doing, and is doing what he feels is the best for the club.
"Danny, being such a young kid who has grown up at Manchester United now going... I think it is a great signing for Arsenal, of course.
"But I'm not a manager and won't be manager of United in the next 10 years, so it's down to the manager there."
Of the arrival of Falcao, a surprise addition to the squad, Beckham is excited.
"I can only speak from my experience of foreign players coming in, and for me, that is what made the Premier League really exciting - to see young talent from England coming through, but also seeing great players like Eric Cantona and David Ginola.
"Without a doubt it inspired me and gave me great experience to see players like that coming to our league."