After a cagey affair in which Blackpool failed to fire it took a slice of luck late in the game to ensure Ince's men maintained their 100 per cent Sky Bet Championship record with a 1-0 win.
Trying to clear a long throw-in into the danger area from on-loan Liverpool defender Jack Robinson, Perkins could not sufficiently clear the ball and it bounced across the line off the bar.
And while Ince conceded he would have settled for a point in the circumstances he was delighted his players kept going until the very end.
"I'd pretty much resigned myself to it being a goalless draw to be honest," said the former England international.
"Though I was disappointed because I felt we created the better chances over the 90 minutes.
"You've got to keep your mind sharp though, and you never know, a chance is always likely to come at the end like that.
"We started well and I thought that if we had scored early on when we were on top, then the floodgates may have opened.
"But credit to Barnsley. They stuck at it and as the clock ticked past 90 minutes I would have taken a point.
"Jack Robinson is dangerous with those long throw-ins, they can be a real weapon.
"I've seen it a lot in training, and I've said to him 'why don't you use it in match situations?'
"He's not just about long throw-ins though. Jack is a very good player, and I know him very well because he came through the Liverpool academy side with [son] Tom.
"He's quick, he's got that quality you need and his decision-making is exceptional.
"We've ground out a result today, but some days you need to do that.
"The spirit and the togetherness is there in the camp, everyone can see that, and I can't for anything more than six points from our opening two games."
Barnsley have now lost two in two in the league following an opening-day mauling at home to Wigan, but were vastly improved today with striker Chris O'Grady twice going close either side of the break.
And boss David Flitcroft admitted defeat was a bitter pill to swallow.
"If Chris O'Grady goes and sticks that chance away just after half-time then it could have been such a different game," he said.
"As we worked hard we're all gutted. It was looking like whoever scored the first goal would go on to win, but to lose it like that is sickening really.
"Up until that late stage in the game we had defended so well. We'd had to withstand throw-ins, corners, free-kicks, everything, but we'd defended heroically.
"It's a difficult one to swallow.
"We created a few chances, but we've not been as slick or nearly as clinical this season yet.
"That's something we'll be working hard on, on Monday morning.
"It's been a horrible way to lose, but I was always surprised at how direct Blackpool were.
"That's been the most direct I've seen them in a long while.
"We've had chances to counter-attack of course, but once one goes in like that right at the death then you're never going to get it back.
"We need to bring in one, maybe two strikers. It's been no secret that we've been trying to do that, but despite some frenzied work behind the scenes nothing is happening just yet."