A controversial late penalty winner by Jordan Rhodes breathed fresh life into Blackburn Rovers battle to avoid relegation - but left The Lions teetering perilously close to the drop zone.
Rhodes sent keeper David Forde the wrong way with just 12 minutes remaining after Mark Beevers was adjudged to have fouled Grant Hanley.
There didn't appear to be any contact by Beevers at the time, and TV replays showed that The Lions had every reason to feel aggrieved as no contact had, in fact, been made.
Speaking about the penalty Jackett said: "I've just seen it again and it did look a soft decision. My opinion is that the referee got his assessment wrong, it didn't look as if there was any contact so I would say it was a harsh decision.
I wasn't displeased with the effort or commitment of my players and whilst we might not have done enough to win the game I certainly think we deserved a point."
To make matters worse, skipper Danny Shittu - one of two Lions players booked for dissent following the penalty decision - was then shown a second yellow card after the final whistle for remonstrating with the ref.
It was a desperate night for Millwall, but it had all started so brightly for Kenny Jackett's men.
Jackett made four changes to the side beaten at Huddersfield on Saturday with Alan Dunne replacing Adam Smith at right-back, Rob Hulse and Jermaine Easter forming a new striking partnership up front and Liam Feeney also drafted in on the right.
The Lions started operating an attacking 4-4-2 formation and looked sharp in the opening exchanges, forcing a couple of corners that the visitors cleared comfortably.
Jack Smith and James Henry had already seen efforts fly narrowly wide before The Lions made the breakthrough.
Henry's deep free-kick from the right was headed back across goal by Mark Beevers, and although the ball was blocked, it fell for Osborne who turned and lashed home an unstoppable shot from 10 yards.
Henry went close to adding a second, but on this occasion Grzegorz Sandomierski tipped his curling free-kick over the bar.
The Rovers keeper also kept out Feeney's deflected shot whilst Hulse headed narrowly wide with Millwall in seeming control.
Rovers, who had barely mustered a shot on goal, came to life as the game headed towards half-time.
David Dunn, later to be stretchered off with an injury, embarked on a clever run to the edge of the area only to fire high and wide.
Then in stoppage time a stinging drive from David Jones was kept out by the athleticism of Forde, who managed to get his fingertips to the ball to turn it round for a corner.
Rovers brought on Josh King for Markus Olsson at the break and Rovers came out firing on all cylinders after the restart.
However their equaliser, when it arrived, was somewhat fortuitous as Jones swung a corner towards the near post which squirmed past Hulse and Henry into the net.
Keeper Forde made excellent save from Dunn but was left shaking his head in disbelief along with the entire Millwall camp when referee Ward pointed to the spot in the 78th minute.
Hanley had set off on a run from deep in his own half and just appeared to run out of steam, stumbling to the floor under what could really be called a tackle by Beevers, who was feet away from the Blackburn man.
Both Forde and Shittu were booked for their protests before Rhodes sent Forde the wrong way from the spot to put Rovers 2-1 ahead.
Millwall pushed on and Osborne came agonisingly close to grabbing a stoppage time equaliser but his shot was kept out by the legs of Sandomierski as Rovers held out for a crucial win.
Forde, Dunne, Beevers, Abdou, Shittu, Osborne, J.Smith, Feeney (Keogh, 77mins), Hulse (Wright, 61mins), Easter (Batt, 61mins), Henry. Subs not used: M.Taylor, Woolford, Malone, Saville.
Batt (64mins), Forde (75mins), Shittu (75mins), Abdou (87mins),
Blackburn Rovers: Sandomierski, Olsson (King, 46mins), Hanley, Jones, Dunn (Orr, 90mins), Williamson, Kane, Morris, Rhodes, Dann, Kazim-Richards (Goodwillie, 15mins). Subs: Usai, Orr, Pedersen, Murphy, Gomes.
Bookings: Hanley (12mins), Dunn (75mins)
Scorers: Jones (55mins), Rhodes (78mins, pen)
Ref: G. Ward
Att: 8,607 (away 240)