While United were wrapping up a loan deal for Colombia striker Radamel Falcao in the last few hours of the summer transfer window, fellow frontman Welbeck - an academy product and England international - was heading out of the club to join the Gunners for a reported £16million.
The Manchester outfit have been famed for their ability to produce young English talent, with the stand-out case being the 'Class of 92', featuring the likes of David Beckham, Paul Scholes, Nicky Butt and Gary and Phil Neville, brought through by Sir Alex Ferguson.
And Phelan, who was Ferguson's number two from 2008 to 2013, told the BBC on Tuesday: "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 Welbeck, there were loan exits from United on transfer deadline day for England Under-21 internationals Nick Powell and Michael Keane.
It remains to be seen whether Tom Cleverley, who has 13 England caps, leaves too, with Aston Villa currently waiting to discover if their move for the midfielder is rubber-stamped by the Premier League.
The Red Devils, with Dutchman Louis van Gaal now in charge, have spent big this summer on a teenage England international in Luke Shaw, and also brought in Falcao, Holland's Daley Blind, Spaniard Ander Herrera and Argentinians Marcos Rojo and Angel di Maria, the latter for a British record £59.7million.
And Phelan added: "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.
"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."
Phelan has also backed Welbeck, 23, to thrive at Arsenal.
"He is still only a young player and with young players you will get peaks and troughs but it is a case of Danny feeling more important in himself than he probably was over the last 12 months," said Phelan.
"He is in a position where he can play where he wants and I think that is why he chose Arsenal because they give him the opportunity to play in his best position, which is a striker.
"A club like Arsenal is a fabulous club, it is a well-run club. From a footballer's point of view, if you want to choose a football club, then Arsenal is right up there with the best."
Beckham, meanwhile, is sad to see Welbeck go, but remains confident Van Gaal "knows what he is doing".
The 39-year-old former United winger and ex-England captain told the BBC: "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.
"Yes, we always worry about the young talent coming through, and obviously seeing Danny leave Manchester United is sad.
"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."