Manchester United manager Van Gaal let Welbeck join Arsenal for a reported fee of £16 million after luring Radamel Falcao from Monaco on a season-long loan deal.
Welbeck scored both goals in England's 2-0 win over Switzerland on Monday and former United players Rio Ferdinand, Paul Scholes and Gary Neville have criticised Van Gaal's decision to let the forward join one of the club's rivals.
But at a press conference with Falcao and fellow new signing Daley Blind on Thursday, the club's new Dutch coach said Welbeck was not prolific enough to stay.
"He played three seasons for the first team," Van Gaal said.
"But he doesn't have the record of [Robin] Van Persie or [Wayne] Rooney. And that is the standard.
"That is why we let him go – because of Falcao – but also to allow the youngsters to fit in.
"That is the policy. That is why I am here."
Welbeck scored 30 goals in 145 appearances in all competitions for United.
