A first-half goal from Jamal Lowe and an own goal by Victor Adeboyejo allowed Swansea, beaten by Derby in midweek, to move up to third in the Championship table.
“The pitch was more of a problem for Swansea than for us,” said Tykes chief Ismael.
“We knew this before the game and it’s awful to say this, but you have to accept it because it’s part of the game in the Championship.
“We were very direct, but we lacked conviction. In some situations, we took the wrong decisions and put ourselves in difficult situations.
“Without big pressure from Swansea, we conceded two goals. I told my guys to keep their heads up and now we have more time to recover for the next game.
“Own goals are part of the game and you have to accept it. I have to try and find a solution after this result but the most important thing was our fatigue.”
Swansea manager Steve Cooper praised the response of his side after they won comfortably.
Both sides were very direct but Swansea had far more quality in the final third of the pitch with their pace on the counter-attack catching Barnsley out on numerous occasions.
“We took a step back on Wednesday, but I don’t want to dwell on it because we put it right today,” said Cooper. “I did see this reaction coming. I saw fire in their bellies in the training ground yesterday – both in the meeting we have with the players and the work on the training ground.
“Myself and the coaching staff said the boys looked ready and there was a really good vibe. It was about offering a little, but it didn’t need much from me today.
“They were ready to put things right and they did that. I am anticipating the attitude we saw today again at QPR.
Swansea took the lead in the second minute when Yan Dhanda headed into the box before Ben Cabango’s flick was drilled into the back of the net by winger Lowe.
Barnsley may have dominated possession but Swansea were constantly catching the Tykes cold on the counter and Adeboyejo headed the ball into the back of his own net from Matt Grimes’ wicked corner.
Swansea City: Woodman, Cabango, Bennett, Guehi, Roberts, Fulton, Grimes, Bidwell, Dhanda, A Ayew, Lowe. Substitutes: Manning, Smith, Benda, Gyökeres, Routledge, Cullen, Latibeaudiere, Cooper, Palmer.
Barnsley: Walton, Sollbauer, Helik, Andersen, Brittain, James (Palmer, 71), Mowatt (Kane, 82), Oduor, Frieser (Miller, 57), Woodrow (Adeboyejo, 57), Chaplin (Thomas, 57).Substitutes not used: Schmidt, Moon, Collins.
Referee: Andy Davies (Hampshire).