The Reds face a Swans side who finished three points above them in the final Championship table and did the double over them with two 2-0 victories at Oakwell and the Liberty Stadium during the regular campaign.
Steve Cooper's side triumphed in Wales just before Christmas and followed up with a professional away-day performance in the fixture in Yorkshire early in the new year.
But Ismael has stressed that his side - who have kicked on in splendid fashion from February onwards - are much improved since both those games.
While the Swans, with a budget far in excess of Barnsley’s, had aspirations to be in the promotion shake-up at the season’s outset, the Reds’ sights were rather more modest after being within a few minutes of relegation at the end of last campaign.
Barnsley’s fates have produced one of the EFL stories of 2020-21 and they are three games away from reaching the Premier League and Ismael has urged his side to have no regrets after both legs against the Swans, who will be the clear favourites and under pressure in his eyes..
Speaking ahead of Monday’s first leg at Oakwell, Ismael said: “We are the underdogs when you see the four teams in the play-offs.
“The other teams have more budget, better players and a bigger squad and depth than us. But we have our principle, desire and beliefs and the player can raise their own performances.
“Mentally, we are really strong and that is why we can compete on the pitch and we are clear underdogs.
“It was not an expectation where Barnsley would be where they are. But this is a reward for the players, who gave everything on the pitch from the first minute to the last. They are completely dedicated to the way we play and our principles.
“When you are focused, organised and believe in yourself and your strengths, everything is possible. The story is not finished. We go in without any pressure.
"No regrets is the motto. We want no regrets at the end of both legs.'
On a third game against Swansea this term - and a fourth - he added: “It is a new competition and it is important we raise the focus and concentration.
“We are motivated to change the story against Swansea this season and we were a completely different team in December when we lost and we changed five regular players in the squad from now and are more confident.
“We respect the quality Swansea have in their squad, but we deserve to be here.”
Ismael has confirmed that Herbie Kane and captain Alex Mowatt - who missed the final game of the regular season against Norwich City as a precaution - are both available for Monday’s game.