Former Tyke Sam Winnall opened the scoring after 50 minutes, pouncing on a mistake by Adam Davies in the Barnsley goal.
Failing to watch the ball out of play, Davies was out of his goal when Adam Reach passed for Winnall to tap into the empty net from 10 yards.
The visitors had several chances to put the tie to bed but Winnall had a goal ruled out for offside and Callum McManaman blazed over from inside the box.
And the Owls were made to pay as Angus MacDonald scored the equaliser deep into time added on, rising highest to meet Adam Hammill’s cross and power a header into the far corner.
Heckingbottom said: “I would have been upset if we had not got something out of the game, but I would have been delighted if we had got three points with the chances at the end.
“It shows the spirit in the team. What could go wrong did go wrong, but it shows the spirit and determination to come out and get something out of the game.
“We know Wednesday are a good side with the ball so we did a lot of work on our shape and I was pleased with it.
“The second half had a lot of tactical shifts and changes in momentum. There were a lot of positives in terms of attitudes and application from the players today.
“If you cut the errors out it would have been a good win for us, so we take the positives whilst still looking at where we can improve.”
The dropped points were a setback to Wednesday’s play-off hopes, but Owls boss Carlos Carvalhal still felt it was a disciplined performance from his side.
He said: “The goalkeepers almost didn’t have a save to make in the first half but in the second half we started to press higher.
“We achieved one goal and should have had more to finish the game. During that period we didn’t feel any real threats to our goal.
“We are training very hard with both offensive and defensive play and we felt there was no real threat to our goal until the end.
“The Sky Bet Championship is a very hard competition. The teams never give up, and it’s good to achieve one goal but it’s important to achieve a second to finish everything.
“If you don’t score the second goal all teams are very strong mentally and believe they can score in the last minutes, which is what happened today.
“We played for the three points and with good discipline. We didn’t play fantastic football but we played with discipline.”