Despite showing plenty of attacking intent and enjoying large spells of possession, particularly in the second period, Parkinson's men suffered their first home league defeat since September thanks to Marley Watkins' second minute header.
Parkinson said: "We've got enough crosses into the box and had enough possession to certainly get something out of the game, so that is a huge frustration for us.
"We have probably delivered more crosses into the box in one single game than we have done for a while.
"We perhaps need that little bit of luck, something to fall our way in the box, but also that extra little bit of devilment in and around that six yard box.
"The main disappointment from tonight (Tuesday) is the start we got off to.
"We've given a side buoyed by winning 6-1 (over Rochdale) at the weekend a huge lift with an early goal.
"It was an avoidable goal, and we only have ourselves to blame. It obviously gave us an uphill task but the effort of the lads was first class - they gave us absolutely everything.
"We just need a little moment of inspiration, a moment of luck perhaps, to go our way.
"We have to keep working on getting balls into the box, getting players in the right position and having them show that final little bit of bravery and composure.
"The crowd were brilliant tonight, absolutely fantastic, and I have to thank them for the way they stuck with the lads.
"We needed to give the crowd a lift tonight and the only way we could do that is play with real intensity in our attacking play. We did that, and the crowd responded.
"We just need something to get us going again at the moment, but no-one is going to hand it to us. We have to work for it as a group and we will do again at the weekend (vs Fleetwood Town)."
Along with the frustration of the Barnsley defeat, Reece Burke and Billy Clarke had to be substituted during the game due to injuries. Skipper Stephen Darby also appeared to be limping towards the end following a crunching 50-50 challenge with Tykes defender George Williams.
Parkinson continued: "Reece has got a problem with his Achilles and Billy Clarke has strained his hamstring.
"It is too early to say how long those two will be out for though.
"Stephen is made of granite so it would have to take something serious to keep him out of the team."