United boss Louis van Gaal opted to sell the England international to the Gunners in the summer of 2014 following his appointment at Old Trafford.
The Dutchman’s decision sparked mixed reactions from United fans, with Welbeck having come through the Red Devils’ youth system.
United have come in for plenty of criticism for their below par form this season and they were eliminated from the Europa League after Liverpool’s 3-1 aggregate victory in the last 16 tie.
And Scholes admits that he is at a loss to explain why Van Gaal opted to let a player of Welbeck’s quality leave Old Trafford in the first place.
Speaking on BT Sport on Thursday night, Scholes said: “Every time I watch United, I keep thinking of the players that have been allowed to leave the club – and you’re just left scratching your head.
“Welbeck’s the biggest example. He should never, ever been allowed to leave this club.
“He’s a big example of what Manchester United are. He was here from nine years of age and came right through to the first team.
“He’s quick, he’s strong, can score a goal, can make a goal, play left wing, right wing, centre-forward… he’d walk into this team now without a shadow of a doubt.
“He’s just been allowed to go. Whether that’s come from the manager or beyond the manager’s dealings, I don’t know. But it should never have been allowed to happen.”
United take on Manchester City on Sunday in the Premier League, while Arsenal travel to Everton on Saturday.
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