The home side went behind in the first half thanks to Conor Washington’s goal, but Luke Berry’s stoppage-time header secured a point for the Tykes.
Peterborough took the lead in the 16th minute through Washington’s close-range strike after Jack Cowgill’s failed clearance had left the striker free to strike hard and low past home goalkeeper Adam Davies from the edge of the six-yard box.
Kgosi Nthle’s second yellow card in the 76th minute helped Barnsley’s case, the defender being sent-off on the back of a crunching tackle on Josh Scowen.
The breakthrough for the home side came deep into stoppage time when Conor Hourihane’s in-swinging corner found the head of Berry, who stooped down low to head past Ben Alwick.
Johnson said: “I was pleased for the players really because the team we put out is going to be different next year, but we need to see if the guys can sink or swim.
“I thought they did alright as a group. It’s fantastic for the club’s academy to have so many academy graduates in the squad and about the place.
“I knew they (Peterborough) were a decent side. I thought our fans were very, very good.
“They showed their maturity, they were educated enough to realise for the greater good of the club that the players needed encouragement to have a good spell.
“I thought Luke Berry did well. He’s been a bit unlucky because he’s come into the club and we’ve got a strong midfield here, there’s no doubt about that.
“It’s probably one of the strongest in the league when they’re at their best, and he found himself out of the side.
“He hasn’t knocked on the door, whether that’s a good thing or bad thing I’ll let you decide, but what he has done is train well.”
Peterborough manager Dave Robertson said: “We managed the game well, but we’ve got to find more concentration for which was essentially the last kick of the game.
“I think it tells you a lot when a team like Peterborough United come to Barnsley, who are used to getting 15,000, and celebrate a goal like they’ve won the cup final.
“That tells me a lot about where we are as a team and I’ll take that as a positive because this is a good club and a big club.
“This was preparation for next year. It will now be about continuing to work on the way that we work together defensively.
“It will be continuing to work on our quality in possession and our bravery to get on the ball, because that’s what I want from our players.”