While the home side have come through games against Crawley Town and Cheltenham Town, the visitors got the better of Sheffield United on penalties in the second round.
While Burnley suffering an away defeat at Leicester City on Sunday evening would have been expected by the majority, the absence of key men highlighted Sean Dyche's predicament with regards to the depth of his squad.
Although the 22-year-old performed admirably at the King Power Stadium, it highlighted that Burnley realistically need to be active in the transfer market over the coming weeks to again challenge for a mid-table spot.
Whether that materialises remains to be seen, but Dyche may feel that he has to use a game such as this one to hand minutes to the other academy players who featured in the squad against the Foxes.
At a time when Burnley appear far from settled, Gary Rowett will be delighted with how his players have started the new campaign in all competitions.
As well as successfully negotiating EFL Cup ties against lower-league opposition, four points and two clean sheets have come from Championship fixtures against Stoke City and Millwall respectively.
There are signs that a lack of goals may be a problem at the second tier this season, with Jed Wallace's strike at the weekend only coming courtesy of an individual error in the Millers backline.
Nevertheless, Rowett will feel that the foundations have been laid ahead of the Lions attempting to build on their near-miss with the playoffs back in July.
Millwall EFL Cup form: WW
Millwall form (all competitions): WDWW
Burnley EFL Cup form: D
Burnley form (all competitions): DL
While some rotation is expected, Rowett is likely to give run-outs to some of the Millwall players who featured among the replacements at the weekend.
With his side having played twice in the space of three days, Dyche will probably make changes for this tie.
Ashley Barnes remains out of contention despite making his return from injury in the reserves.
Millwall possible starting lineup:
Bialkowski; Romeo, Hutchinson, Cooper, Wallace; Mahoney, Woods, Leonard, Ferguson; Smith, Bodvarsson
Burnley possible starting lineup:
Peacock-Farrell; Lowton, Long, Dunne, Taylor; McNeil, Westwood, Brownhill, Pieters; Rodriguez, Vydra
We say: Millwall 1-1 Burnley
This games has the potential to be somewhat of a war of attrition, something which we feel will lead to the game ending in a low-scoring draw. With the belief that they have from their shootout success last week, Burnley could prevail on spot kicks.