David McGoldrick’s double condemned the Lions to a seventh Championship game without a victory, despite Billy Sharp missing a first-half penalty.
The Blades striker atoned to score the opener but Jake Cooper and Lee Gregory found the net for the hosts within the first five minutes of the second half.
Yet Millwall crumbed as McGoldrick scored a penalty and then netted with two minutes to go, with Harris issuing a rallying cry for leaders to emerge from within.
“These late goals must be down to concentration in the group and a winning mentality,” said the manager.
“You can talk about bad luck or good goals against us, but these were poor goals and people not doing their jobs – that’s what it boils down to.
“If the dressing room has anything about it, now, they should lift themselves.
“If they want to do their jobs properly, and they want to be considered for team selection, they need to show more leadership and more quality in themselves in key moments.
“It might sound a little bit harsh, but it’s time for harsh words. We’ve thrown points away again.
“The table doesn’t lie, it never lies. We have to do what made us so good last year. Ultimately individuals have to perform better than they are.
“I’ll do my job, I’ll make sure the players are prepared to play Nottingham Forest Wednesday night.”
Millwall remain stranded in the relegation zone after McGoldrick tucked home from three yards two minutes from time, after scoring from the penalty spot ten minutes previous after a foul.
Sharp had earlier put the Blades in front, atoning for missing his own spot-kick thanks to a wonderful save from Ben Amos following a hand-ball.
But, after the home crowd made their feelings heard at half-time, Cooper headed home from a corner just two minutes after the restart to level up the contest.
Gregory then ran on to a ball over the top and finished to put his side ahead on 50 minutes but United battled back, a position boss Chris Wilder felt should have been avoided.
“It shouldn’t have been a nail-biter,” he admitted.
“We had to be right at it. For five minutes we weren’t and we got punished. But for the majority of time we were and we all played our part in what I believe was a deserved victory.
“If we’d have walked away with two each I would have been delighted with the way we played. Credit to them.
“The momentum is gone, the place is rocking and it’s changed from a comfortable afternoon to one that’s going to be difficult.
“I’m just glad we don’t have to come here because it is such a difficult place to play. No doubt they’ll get a result and they’ll be up and running.
“They’re a tough team no matter how you look at it. They’ve got too many good players, too many honest professionals that want to run around and get a result.
“Millwall will find a way to win, without a shadow of a doubt.
“We’re delighted with 19 points after 10 games but that can quickly change if things aren’t right.”