The 23-year-old joined Arsenal on Deadline Day for £16 million, meaning Louis van Gaal's side were willing to part with Welbeck on a permanent basis - not just on a loan deal as many were expecting.
But Carragher has questioned the logic behind allowing the England striker to leave Old Trafford.
Indeed, according to the former Reds defender, Welbeck possessed the one quality Man United no longer have: pace.
Speaking to Sky Sports News before the forward's move to north London was confirmed - but when United were believed to be intent on selling the 23-year-old, Carragher said:
"Well, I think it's a strange one, in the fact that Danny Welbeck's got a lot of pace in his game and the one thing I'd say about Man United in the last 12 months or so is that they've lacked that within the team.
"I think [Angel] Di Maria will add that, he's got pace, he's got energy. But Welbeck is one of the players within the squad that adds that pace and energy.
"I don't think Welbeck's ever going to be in the category of [Wayne] Rooney, [Robin] Van Persie or [Radamel] Falcao but he's a great player to have within your squad.
"He can play two or three positions, he gives you that pace and I think people will be slightly disappointed he's gone, especially from an England perspective."
Arsenal boss Arsene Wenger, of course, will be hoping Manchester United's loss will prove the Gunners' gain, as the north London side are in desperate need of cover for the injured Olivier Giroud.
Yaya Sanogo has so far failed to deputise adequately for the Frenchman in the Premier League, while £35 million summer signing Alexis Sanchez is not a natural centre-forward.