Tykes midfielder Jim O'Brien scored the only goal of the game at Oakwell, slotting home his third of the season in the fourth minute after collecting Martin Cranie's long ball and rounding Lions goalkeeper David Forde.
The result leaves Millwall a place outside the drop zone, two points and two positions above Barnsley.
Holloway said: "We've got to stick together as a team. We've got 14 games left, things have got a lot harder after today but they were going to be hard anyway.
"We stayed up by one point last year, does anybody see it any differently (this year)? It might have been different if we'd got the right result today.
"And, after four minutes, one long ball from a centre-half goes straight over our heads and they score. It couldn't get any harder, could it?
"I'm upset with the result, some of the stats will tell me some of things were okay but you need to put the ball in their net and stop it going in yours and, at the moment, we've had a season full of those things going the opposite way.
"Things would have been a damn sight easier if we'd kept them further away from us but not now.
"We lost three points today; even a draw would've done us, even a draw would've kept them away from us but now that's given them a chance, that's lifted their spirits and we've just got to show some character, which our club is full of.
"At the end of the day no one's died today, although it might feel like it."
Barnsley assistant manager Micky Mellon praised his side's performance after they secured an important victory.
Mellon said: "We know the value of three points at this time of the season and it was much-needed against one of the teams that are down there with us, so I'm delighted to get the result today and collect all three points.
"There was a lot of big performances there and it's those types of performances that are required at this time of the season and we're well aware of that."
Mellon said he was unconcerned by wins for the other two sides in the relegation zone, Yeovil and Charlton.
He added: "We're not good enough to think about anybody else; we've got to worry about what we do, concentrate on that.
"It won't affect us what anybody else does as long as we keep our part of the bargain and do the business.
"There're more teams than us in it, you've got to focus and concentrate on the very next half (of a match), break it down as much as that, and do well in it.
"It's tough; it's the Championship and anybody can beat anybody. We've just got to make sure we do the basics well and hopefully our big players turn up on the day and get results like today for us."