Ben Maund's tap-in after only four minutes was the only goal of the game which was played on a very heavy surface.
Despite the difficult conditions, the game started with a very quick tempo and after the Sky Blues forced an early corner, Ben Maund was on hand to tap in a rebound with the Reds' defence stood still.
Barnsley responded well and had their first of 20 attempts on goal on 10 minutes as Danny Rose's header was planted wide after he connected well with Reuben Noble-Lazarus' wicked cross.
Rose had an even better chance on 21 minutes to level things up but as he raced in on goal and with the 'keeper off his line, his lofted attempt drifted wide of the far post.
It wasn't a case of third time lucky for Rose, either, as his looping header from eight yards was expertly tipped wide by City 'keeper Burge on the half-hour mark.
After the break the Reds continued in their search for an equaliser but it was to no avail, Paul Digby's 25-yard free-kick denied once again by an inspired City 'keeper in Lee Burge.
"I'm very pleased with the performance," said Academy Coach Chris Howarth. "I thought the application of the lads on a poor pitch was very good. I'm just disappointed that we couldn't stick the ball in the net.
"Other than their goal, performance-wise we were excellent. Their 'keeper has made three really good saves in the game but our lads have got to finish. You get confidence from scoring goals and you want lads like Danny (Rose) to come off the pitch having scored two or three.
"They're pushing all the time which is what this football's for. We're developing the players but we want to develop a winning mentality. They're gutted because they've had chances to score. I'm glad they're gutted because had they come off happy as Larry having not got a result despite playing well, then you've got a problem on your hands. Obviously the desire is there to want to do well. From a Coach's point of view you can't ask for much more than application from your players. If you come in every day and work hard, you're going to get better."
Reds: Dibble, Smith, McKnight, Trialist, Jones, Abbott, Clark, Digby, Sousa, Noble-Lazarus, Rose.
Coventry: Burge, Phillips , Urquhart, Finch, Haynes, Slager, Barton, Lawton, Rankin, Maund, Garner.