Jay Rodgriguez secured a classic smash and grab raid with a 37th-minute winner for Burnley - but The Lions were left wondering what might have been after having a couple of penalty appeals turned down in the second half.
England U21 international winger Rodgriguez swept home the decisive goal after The Lions failed to deal with a Ross Wallace corner in an otherwise forgettable opening period.
But Millwall picked themselves up and battered Burnley after the break, with referee Steve Hooper waving away two shouts for a penalty when sub John Marquis was impeded in the penalty area.
Clarets keeper Lee Grant made tremendous saves to deny Liam Feeney and Brian Howard, Marquis had a goal disallowed for offside and then saw his late header cleared off the line as The Lions' just could not find a way through.
Whilst obviously disappointed at a fourth successive defeat, Den boss Kenny Jackett was measured in his assessment of the game and the overall situation.
He said: "The first half was fairly even, but we gave away a poor goal and that was very disappointing.
We did enough and showed a lot of spirit. We are still missing that little bit of luck.
I felt we should have had a penalty. John (Marquis) has worked himself a good position and the defender's stuck out a leg but the ref's not given it. We need that bit of good fortune for a decision to go our way.
The reality, looking at it from the sidelines, is I think we can match Burnley in most areas, but I still haven't adequately sorted the forward situation. One goal in seven League games speaks for itself and I have to do something about it."
Lions Player subscribers can see the full interview with Kenny in which he talks about solving Millwall's goal drought.
Millwall: Forde, Mkandawire, Barron, Trotter, Robinson, Ward, Feeney, Howard, N'Guessan, Simpson (Marquis, 46mins), Henry (Bouazza, 72mins). Subs not used: Mildenhall, Abdou, Dunne.
Bookings: Howard (53mins), Marquis (77mins)
Burnley: Grant, Wallace, Easton, Amougou, Edgar, Trippier, Stanislas (Treacy, 78mins), McCann, Bartley (Marney, 73mins), Rodriguez, Austin. Subs not used: Stewart, Mee, Hines.
Bookings: Trippier (45mins), Bartley (69mins), Easton (85mins)
Scorer: Rodriguez (37mins)
Ref: S. Hooper
Att: 10,460 (away 574)