The stand-in skipper received his marching orders for a high tackle on Adam Hammill on 63 minutes, shortly after Michael Owen had handed United a two-goal lead.
Danny Welbeck had earlier opened the scoring for the holders, but the game may be remembered for referee Chris Foy’s red card decision, for which Ferguson has no complaints.
“I’ve just seen it here and I think he probably has followed through,’’ Ferguson said.
“He’s caught the boy, not high, but just above the ankle and I think that in the present climate the referee is probably correct.’’
Ferguson refused to dwell on the incident, instead focusing on his young side’s promising performance against a determined Barnsley team.
He added: “Well it was a cup tie and Barnsley have worked very hard. They put a lot of effort into the game and they had one or two chances after we went down to 10 men.
“I think at the end of the day we’ve just about got through and probably deserved to get through.
“We didn’t play as well as we could have, but we are through and happy with that.”
Ferguson named a completely different starting XI to the one which went down 2-0 to Liverpool on Sunday and the youngsters rose to the challenge at Oakwell.
Ferguson added: “When you’re playing away from home in a cup tie it’s a different experience than playing in Old Trafford.
“Last year when we won the cup we got a lot of home draws until the semi-finals when we had an away game with Derby County of course.’’
Michael Owen was in the thick of the action in the final third for United, finally finding the net just before the hour mark with his first shot on target.
“It’s a fantastic goal, unbelievably good feet, quick and a marvellous finish. It was a great, great goal,’’ Ferguson said of Owen’s 59th minute strike.
With the experienced Owen leading the line ahead of youngsters Welbeck and Federico Macheda, it was Welbeck who opened the scoring with a near-post header after just six minutes.
However, the 18-year-old was forced to withdraw shortly after the break after picking up a knock in the first half, but Ferguson does not believe the injury is too serious.
“He got an injury in the first-half,’’ he said. “We thought we’d try him in the second but after a few minutes we knew it was no use so Zoran (Tosic) came on to replace him. We’ll scan it tomorrow.’’
Barnsley manager Mark Robins felt his side showed United too much respect.
The former United striker said: “We were on the back foot to start with I felt.
“Mentally, when you come up against Manchester United you probably give them too much respect and we were on the back foot because we conceded an early goal from a set piece.
“But they’ve got quality everywhere, whichever side they put out, but I just felt there was more in us.
BARNSLEY: Steele, Kozluk, Moore, Foster, Julian Gray, De Silva (Campbell-Ryce, 71), Colace (Butterfield, 77), Hallfredsson, Hammill, Macken (Hume, 65), Bogdanovic.
MAN UTD: Foster, Neville, Brown, Jonathan Evans, Fabio Da Silva, Obertan, Rafael Da Silva, Anderson, Welbeck (Tosic, 53), Macheda, Owen (de Laet, 65).
Referee: Chris Foy (Merseyside).