The only downside for Ferguson was Gary Neville's sending off in the second half for going through the back of Adam Hammill.
Ferguson, who made 11 changes to the team that lost to Liverpool, told Sky Sports: "Barnsley worked very hard and put in a lot of effort and they had one or two chances after we went down to 10 men.
"But overall I think we deserved to win the game and I'm delighted with the response from the players.
"We didn't play as well as we could have, but we are through and happy with that."
Owen finished superbly after being released by Fabio and Ferguson said: "It was a fantastic goal, he had such quick feet, it was a marvellous finish."
However the former Newcastle striker remains irritated by what is expected of him.
"A start and a goal, you can't ask for more than that, " he said. "It is how people judge me unfortunately.
"I started a game against Bolton and was pretty pleased and thought I played pretty well. Then I looked at the papers and was given a three or four.
"But in this game I played pretty average and scored a goal and I'll probably get seven out of 10.
"I think I deserved a five in this game and seven or eight from the Bolton game."
Ferguson had no quarrel with referee Chris Foy for handing Neville a straight red card.
He added: "I've just seen the sending off, and Gary did follow through with the tackle and caught the player.
"It was not high, just above the ankle, but in the present climate I would say that the referee was probably correct."
Barnsley manager Mark Robins felt his side showed United's second string too much respect and have plenty more to offer in their bid to climb the Championship table.
The former United striker, who spent six years at Old Trafford before moving on to Norwich in 1992, believed poor finishing prevented his side making a better fist of it.
Robins 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.
"If you look at the stats we had 17 efforts on goal and you'd be hard pressed to find any side that creates that many chances against a Manchester United side.
"On a downside we haven't taken any and you've got to take your chances."
Skipper Stephen Foster headed against the angle of post and crossbar in the first half and Anderson De Silva and Iain Hume, with his first touch, also went close for the Tykes.
Robins added: "United had four or five chances on the night and scored the two. They had plenty of possession, but we defended well, I just felt we were lacking that bit of belief.
"There's more in there for us. There's more in the players, so there are positives."