The Iron's home form is becoming a real concern, and they made life too easy for the Welsh visitors.
Jay Bothroyd opened the scoring in just the second minute and Michael Chopra doubled their advantage seven minutes later.
Bothroyd had made it three before goals from on-loan forwards Kevin McDonald and Dany N'Guessan hauled the Iron back into the match.
By then the damage was already done, and Seni Olofinhana grabbed a late goal to end hopes of an Iron comeback.
"We spent all week preaching to the players the need for us to get away to a good start, particularly against a team like Cardiff," said Baraclough.
"But we were a goal down inside a minute before any of my players had touched the ball or got anywhere really near it, when you're 3-0 down in little more than half an hour a lot of things go through your mind, including the thought of a cricket score.
"We showed great character to get ourselves back into the game but everything that we did in the second half pales into insignificance after what had gone on before.Our home form really is becoming a problem, we desperately want to do better in front of our own fans."
Dave Jones, the Cardiff City coach, felt his side should have opened up an even greater advantage on the back of their first-half display.
"It looked like it could have been a rout in the first half. We could have made life a lot easier if we had scored more goals when we had the chance. But it was some sloppiness and laziness on our part which let Scunthorpe back into the game just before half-time.
"Credit to them, they then had a real go in the second half and made a real game of it. It's good to get back in winning ways for us."