The Austrian, 47, was appointed in the summer to replace Valerian Ismael, who joined Championship rivals West Bromwich Albion, but he struggled from the outset.
The defeat at Ashton Gate, which came after the Reds had taken a 28th-minute lead through Aaron Leya Iseka, extended Barnsley’s miserable sequence to 13 matches without a win – the longest under one manager in the club’s history.
The hosts were hardly in good form themseleves coming into Saturday’s game, but two goals just before the break from Andreas Weimann saw the Robins come from behind to register the first three-point haul on their own ground since January.
In all, the unhappy sequence stretched back 18 games, only three of which came before manager Nigel Pearson’s appointment.
And it looked like being extended when Iseka shot Barnsley in front from Devante Cole’s cross on 28 minutes.
But Weimann burst through the middle to bury the equaliser past Brad Collins on 41 minutes and struck again with a precise side-footed finish in first-half stoppage time.
Schopp saw his side denied by some fine saves by goalkeeper Dan Bentley and several goal-line clearances, while Liam Kitching hit the crossbar in the second half, leaving a frustrated Schopp to insist: “The ball just wouldn’t go in for us.
“We have paid for a five-minute spell before half-time when we didn’t look after the ball well enough. Perhaps we still lack a bit of experience in that situation.”
Hinting that the defeat could spell the end for his Oakwell reign, Schopp added: “Other than that, I couldn’t have asked more of my players. We are so near to where we need to be and I hope I am given more time to work with them.
“That is out of my hands. We couldn’t have created more chances than we did today and at times it was hard to see how the ball stayed out of their net.
“All that was missing was the result. I know that is hard for our fans to accept and they are suffering along with everyone at the club. But I repeat that we are nearly there. There is still a bit to do and no one wants to hear that when you are struggling.”
Bristol City: Bentley, Tanner, Kalas, Atkinson, Pring (Dasilva 50), Massengo, James, Bakinson (Benarous 67), Weimann, Martin, Wells. Unused substitutes: Simpson, O’Dowda, O’Leary, Bell, Scott.
Barnsley: Collins, Andersen, Helik, Kitching, Brittain, Gomes (Benson 46), Moon, Jordan Williams, Cole, Woodrow, Iseka (Adeboyejo 75). Unused substitutes: Walton, Sibbick, Palmer, Oduor, Frieser.
Referee: Thomas Bramall (Sheffield).