David Syers plundered a hat-trick, while leading marksman Sam Winnall struck with his 17th goal of the season and fellow striker Paddy Madden scored his first for the club since his January move from Yeovil.
Substitute Michael Drennan headed an 84th-minute consolation goal for Portsmouth, who had lost only one of their previous five away games.
"I made a couple of changes at half-time, but to be honest I could have taken more off than just the two," Barker fumed.
"We went through all our preparation work in midweek to prepare them for Scunthorpe and yet we get a performance like this.
"We were outfought and outplayed by a Scunthorpe team who were mentally much stronger than us.
"They were more ruthless than us. They won every tackle and every second ball - and they were still chasing lost causes when they were 5-0 ahead.
"We have some players here who seem to think they are too good for that.
"To go 16 matches without defeat, like Scunthorpe have, you obviously have to be mentally strong and have the right desire.
"They are in a good place at this time. They have better players than us - but that is no excuse for the way we performed.
"We obviously have not got enough of the right people at this club with the desire that is needed.
"We are just papering over the cracks at the moment, waiting for the season to come to an end."