Jordan Willis grabbed the only goal of the game as Coventry earned back-to-back league victories for the first time this season.
As a result, Barnsley extended their 95-year winless sequence in Coventry to 25 matches.
German head coach Stendel, who had seen his side register four wins and three draws to move into third place, said the Sky Blues had given them a different test to other rivals.
“In the other games we’ve played most of the teams have stayed deep, only defending, so it was very difficult to create chances. This was different because Coventry have good, quick players and it was a very good test for us to see how we can play against a good team.
“We didn’t have to lose this game because we had enough chances but we gave Coventry too many chances to score.
“We’re not very satisfied with our game but Coventry played well.”
Coventry City manager Mark Robins claimed ahead of the game at the Ricoh Arena that a club he used to manage are one of the best in the division.
But Conor Chaplin should have given Coventry an early breakthrough when he somehow side-footed wide from six yards.
Chaplin joined Coventry from Portsmouth on deadline day after being a target of the Reds and a rueful Stendel said: “We saw that Conor is a very good player – it would have been better if he had played for us today!”
Jacob Brown also spurned two clear-cut chances for Barnsley, firstly when he intercepted Junior Brown’s backpass only to see goalkeeper Lee Burge touch his low shot onto a post before firing wide when well-placed from Mamadou Thiam’s low cross.
Burge tipped over Thiam’s 20-yard curler five minutes into the second half, but City were denied when Chaplin’s fierce finish was disallowed for offside in the build-up.
An end-to-end affair saw scrambles in both areas but City grabbed the winner when Michael Doyle’s free-kick was headed back inside by Dominic Hyam and Willis bundled in from close range.
Coventry: Burge, Sterling, Willis, Hyam, Brown, Thomas (Bakayoko 89), Bayliss, Doyle, Shipley (Kelly 68), Chaplin, Clarke-Harris. Unused substitutes: Davies, Hiwula, O’Brien, Andreu, Thompson.
Barnsley: Davies, Cavare, Pinnock, Lindsay (McGeehan 83), Pinillos, Bahre (Moncur 65), Dougall, Mowatt, Thiam, Brown (Adeboyejo 72), Moore. Unused substitutes: Walton, Bird, Jackson, Ben Williams.
Referee: T Kettle (Rutland).