Cardiff lost 2-0 at home to the Tykes at home on Saturday having drawn 1-1 there with West Brom on Tuesday.
"It's not a test of my management skills at all. It's a test of the players' character and mentality now to dig in," said Jones.
We handed them the game - Jones
"We didn't have it against Barnsley, but we had it the other night [against West Brom]." Financial constraints prevented Jones signing any players during the January transfer window, leaving him and the club's fans disappointed.
That has left Jones with relatively limited playing resources and the fear that fresh injury problems could undermine the club's ambitions for a place in the Premier League.
But Jones says his players must still apply the basics of communication and concentration to their performances.
He said: "If you want to get out of this division and go and play in the next division, then concentration is a major part of the game, communication's a major part of the game.
"We didn't really do a great deal of that [against Barnsley] and that's why we let ourselves down.
"We just didn't do enough, full stop. Credit to Barnsley, they'll feel like they played well and everything else, but we didn't really get at them and everything else and we're at home and we've got to do that."
Defender Anthony Gerrard was replaced at the break after suffering a blow to the head.
I think the whole back five got some sort of bang [on the head] before they went out, because they were all over the place in the first 20 minutes
Jones said: "He just got a bang and was a bit all over the place, but I think the whole back five got some sort of bang before they went out, because they were all over the place in the first 20 minutes.
"And that's where you just need a bit of solidness, a little bit of know-how to say, 'hey, let's just keep it tight here and not give something stupid away'.
"But we'll get back on the training ground and we'll show them again and we'll work at it again and that's what we've got to keep doing.
"But you can't make the mistakes we made and expect to get away with it."
The Bluebirds travel to Preston on Saturday hoping to redeem themselves and return to winning ways.
Source: BBC Sport
Source: BBC Sport