The US international went down once in each half under the challenges of Owls players Tom Lees and Joey Pelupessy, but referee Tim Robinson was unmoved.
A first-half 'goal' from Cauley Woodrow after Wednesday failed to defend a corner from Alex Mowatt was also ruled out, to the disappointment of Ismael.
Legitimate strikes either side of half-time from Jordan Rhodes gave relegation-haunted Wednesday a shock 2-0 lead at Oakwell and while a late Carlton Morris strike gave the hosts hope, the spoils went to the visitors, who extended their unbeaten run in Barnsley to seven matches.
In the process, it inflicted a first defeat in 13 matches in the league upon the fifth-placed Reds, who had won nine of their ten previous games.
Barnsley now head into the international break before their return to action, a key home encounter against Reading at Oakwell on Good Friday and Ismael admits it is well timed.
Ismael, who confirmed that Herbie Kane missed the game with a knee injury, said: “For sure, we are disappointed to lose the game, especially the derby game. We know what this means for our fans.
“But we have to stay fair. Sheffield played better and deserved to win. This is the simple truth.
“You could see the fatigue and freshness was not on the pitch as we made two mistakes to concede goals. It is all concentration and we showed tiredness and it made for a difficult game.
“I have to say that even though we played bad, we should have had two penalties and we had one goal disallowed and nobody knows why when you see the pictures.
“That is why even though it was not a good day, if the referee does his job, you can win the game or at least stay in the game.
“I could not see any faults (with Woodrow’s) goal. It was a surprise for us that the goal was disallowed and there were two clear penalties, no discussions whatsoever.
“But my job today is to have more of an overview of the situation. The way we have performed since Chelsea, we have played a lot of games every three days and the guys perform at a very high level and we are very proud of the performance.
“It puts us in a brilliant position.
“To come back at Bournemouth was an unbelievable performance and then to win at Wycombe and the mentality.
“Today, we had not to make mistakes and keep the game alive and use your chances. But we made two mistakes.”
Emphasising the need for players and staff to now recharge their batteries for the run-in, the Frenchman added: “We now need to recover. It is clear that the international break is a big welcome for us and now it is time to recover, see the family and re-set ourselves and come back with big freshness and a mindset for the last eight games and the last effort.