United’s former assistant Manager, Mike Phelan, also feels part of the club’s “identity has been broken” with Welbeck’s departure to Arsenal.
Striker Welbeck, who came through the Old Trafford youth system, joined the Gunners for £16m on transfer deadline day.
United however brought striker Radamel Falcao on a £6m loan deal from Monaco, their sixth signing of the transfer window.
“Arsenal have a very good, young talented English player,” said former United midfielder Beckham.
“To see him leave Manchester United is sad. He had been there since he was eight and his heart was in Manchester.”
The former England captain added: “Manchester United have always bought players in but also have had a great scouting system which Sir Alex Ferguson put in quite a few years ago, where we did create home-grown talent, and that is something we have done over the years.”
Welbeck is currently away with the England squad ahead of their friendly with Norway on Wednesday as they prepare for next Monday’s Euro 2016 qualifier against Switzerland.
“They have probably lost the way of Manchester United a little bit,” Phelan told BBC Sport.
“Now, rather than produce, it may be the case where they are buying in.
“Someone like a Danny Welbeck has been part of United’s identity and that has been broken.
“What will happen in the future now, nobody knows but that thread has been broken now.”
As well as Colombian Falcao, new United boss Lois Van Gaal has also brought in Angel Di Maria for a British-record £59.7m, midfielder Ander Herrera for £29m from Athletic Bilbao, left-back Luke Shaw in a £27m from Southampton, the £16m Marcos Rojo from Sporting Lisbon and midfielder Daley Blind from Ajax for £13.8m.
But Phelan, who was Ferguson’s assistant between 2008 and 2013, believes the big-money arrivals at Old Trafford could suggest a change of philosophy at the club.
“There is always the start of something and maybe this is the start of a new way of doing things at Manchester United and maybe that is the way football is going,” he added.
“Is it better to look at the instant rather than the future? It is a difficult one because youth is always the future, we all have to start somewhere and you just hope that product of youth can develop in the Premier League.”