Beckford grabbed Everton's second goal after Louis Saha had got the Toffees off to a fine start at Glanford Park with a fourth-minute strike.
Michael Collins pulled one back against the run of play as Scunthorpe briefly threatened a fightback but goals from Seamus Coleman, Marouane Fellaini and Leighton Baines killed them off.
Baraclough, who played alongside Beckford for the Iron, said: "He looked bright and didn't look out of place in their team.
"I just hope he can prove himself to be a good striker at that level, because he is a good striker.
"It is all about confidence. Jermaine could have gone in there thinking it is all too much for him but it certainly isn't.
"I'm pleased for him. I'm disappointed he scored today, obviously, but he is a good kid and deserves success."