Following Tuesday's disappointing home loss to Gillingham, Parkinson has demanded that his players up their game for the trip to South Yorkshire this weekend.
Parkinson said: "We need to do a lot better than we did on Tuesday.
"As I said after that (Gillingham) game, the performance that night didn't reflect what we are all about.
"We need to put that right on Saturday.
"We sat down with the players and went through the Gillingham game with them this week to make sure they are aware of the points they need to do much better.
"If we play to our maximum on Saturday but we don't get the points, I can still live with that.
"When we don't play like we can, when we don't show the right levels of determination, that doesn't sit very comfortably with me or the rest of the staff."
Since the Gillingham game, Parkinson has moved to bring in West Ham United defender Reece Burke and Wolverhampton Wanderers midfielder Lee Evans on loan.
The pair are likely to be in the squad for this Saturday's fixture at Oakwell, although Frenchman Christopher Routis is sidelined with the hamstring injury he picked up against Gillingham.
Parkinson added: "They are both good lads and two young hungry players for us to add to the squad.
"Both of them want to impress.
"Reece had a spell in West Ham United's first team towards the end of last season.
"Lee had a period in the Championship with Wolves last year as well. He also played his part in their promotion from League 1 a couple of seasons ago.
"They come here keen to do well and ready to fight for a place.
"We feel some players that have been in the team recently haven't taken their opportunity.
"My message to the eleven selected at Barnsley on Saturday is simply 'stay in the team'.
"Make sure when we are contemplating our team for Port Vale next weekend, your name is near the top of our list.
"I want to see fight from the players - on and off the pitch - to make sure they keep hold of their shirt."