The game was settled by a first-half strike from Dominik Frieser coolly slotted home the only the goal of the game on 39 minutes after being played in by the excellent Romal Palmer.
It was the Austrian's first strike on home soil after failing to find the net at Oakwell last term.
But the encounter ended in dramatic fashion, with the Reds indebted to a huge late penalty save from Brad Collins after a controversial decision.
It came after Jordan Williams challenged Jamie Allen, with the penalty awarded on the call of an assistant after John Busby initially did not chose to penalise the tackle.
Collins kept his composure to make a superb save to keep out the spot-kick by Viktor Gyokeres, who had earlier clipped the crossbar with a first-half effort.
The Sky Blues, led by ex-Reds boss Mark Robins, had dominated swathes of the game after Barnsley's opener, but the hosts held out as Schopp was left to savour the first victory of his reign on the day that fans returned to Oakwell.
The Midlanders also went very close on the restart when Coventry defender Michael Rose saw a header cleared off the line by home captain Cauley Woodrow, but Frieser's strike proved the difference, although victory was marred by the sight of Morris, a major player for the Reds, being substituted in the first period.
Morris watched the second half from the West Stand and was wearing a leg brace.
Schopp said: "Right now, I don't know. I came from the locker room and did not get any information, but I definitely will when I come back later.
"It is always concerning when a player comes from the pitch early and of course, I am concerned. But it is too early to give any information."
On the victory and a dubious penalty award, Schopp, whose unbeaten side, with four points from two matches, welcome Luton Town on Tuesday night, continued: "It is so important to start with three points in our first home game.
"It was an important three points, but in the end, I know we have to improve in a lot of situations.
"Coventry did play really well and we were struggling to win the balls in the areas where we wanted to and to find good solutions. But we knew when we won the ball that Dominik is a player who is always dangerous.
"We had previously had two situation where he attacked from deep and we didn't give the ball to him and at the next moment, Romal did an awesome job, giving him the ball in the right moment. I am so glad for Dominik that he scored. He gives us something that we need and his runs from deep are always dangerous."
And on the late penalty award, he said: "When you get a late penalty (against you), it is always a tough one.
"But I guess it is a moment that each goalkeeper is waiting for and it can bring something special to the team. To save a penalty when a team is 1-0 up is a big thing and I am happy for him.
"For a young team, it is so important to start with three points. It is easier when you have a couple of points in the table."