Although goals from Ian Morris and Kelly Youga gave the Iron a two-goal advantage, the Tykes came back into the game and levelled deep in second-half stoppage time.
And although Adkins was gutted to miss out on a vital three points, he was pleased with the display following Saturday's 5-0 reverse at The Hawthorns.
"I thought we played some great football and created numerous opportunities," he said.
"No-one would have expected the players to have perform the way they did after what happened to us at West Brom so the morale of the side isn't a problem.
"No-one is going to feel sorry for us and I'm not going to allow anyone to throw the towel in because that's what life is all about."
"It's the fourth game in 10 days but to play the way we did in the first-half was commendable.
"It was pass and move and we did that in abundance, in the second-half the goal that they scored gave them a lifeline.
"They pressed, got the ball forward and pressed. With all the will in the world we tried to keep them out, it never happened and then in injury-time a refereeing decision again has given them a penalty.
"Yes the ball has hit Andy Crosby's hand, but he doesn't know anything about it and the referee has given the penalty.
"We try to play football but at the end we could have done with an ugly, get the ball out performance. We tried that but didn't do it very well.
"We need to keep the spirits up as much as we can. We're allowed to be down today but we'll pick that emotion and turn it around.
"We'd have liked to have been on 30 points at this stage but we're on 27 so we're a little bit short of where we want to be.
"But we have to take where we are. The performance and the effort was worthy of a victory but we're allowed the emotion of being down."