A Grant Hall own goal proved the difference between the two sides as Boro failed to build on their home wins over Stoke and Preston.
The result leaves the Teessiders six points off a play-off place with eight games remaining, after top-six rivals Reading and Bournemouth both dropped points.
Boro now have to wait two weeks until their next game when they’ll travel to the Vitality Stadium to face Bournemouth, who are three points ahead of them in the table.
Warnock was far from impressed with his side’s performance against Millwall and made three substitutions at half time.
After a poor first-half display, Boro did improve after the break, yet a lack of quality in the final third proved costly.
Here’s how the visitors fared at The Den.
1. Marcus Bettinelli - 7
Made a couple of fine saves to keep out efforts from Jed Wallace and Jón Dadi Bodvarsson. 7 Photo: Alex Burstow
2. Djed Spence - 4
Sloppy in possession and lost the ball for the goal. Subbed at half time. 4 Photo: Getty Images
3. Grant Hall - 7
Unfortunate to score the own goal when Boro were cut open. Was solid for the rest of the game and dominant in the air. 7 Photo: Stu Forster
4. Dael Fry - 7
Kept Millwall frontman Mason Bennett on the fringes for most of the game. Wasn’t much movement in front of him in the first half. 7 Photo: Getty Images