For the second game running, Swansea broke the deadlock with a brilliant 39th-minute strike with Matt Grimes following up Andre Ayew's classy opener at Oakwell to put the Liberty Stadium outfit 1-0 up in the second installment and 2-0 up on aggregate.
Barnsley made a real fight of it in the second half and eventually drew level through Cauley Woodrow, but try as they might, they could not add a second goal to draw level on aggregate.
Ismael said: “Congratulations to Swansea, they deserve to be in the final. When you see the two games, they were really really clinical.
“Their first shot on target in the first leg was in and today, only shot on target was in. If you score one goal you deserve, it is as simple as that.
“We did our job and scored our goal away and wanted to stay in the game all the time and we kept alive and we can be proud of our performance and showed why we are in the play-offs and it is not a surprise. We deserve to be here.
“We fought until the end and for sure, we are disappointed. But we have time to reflect on how we reached this season with the squad with one of the lowest budgets in the league and the youngest team in the league.
“I want to thank everyone at the club and the staff for their commitment. They were all dedicated, the players, the background people and our fans for their support on Monday. We can be proud.
“You can imagine that it was a big disappointment (in the dressing room). But they gave everything and can stay proud. Swansea scored two goals and the quality made the difference; it is as simple as that.
“They scored in the same minute of each game and one they scored, it was enough. They were really dfsciplined and did not make any mistakes and we have to accept this.