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He said: "We have three home games on the trot now and if we can take the points we will be up there in the top six and I believe we have the ability to stay there."
Meanwhile, the problems are piling up for Blackpool manager Simon Grayson, who saw his side slip to their third successive league defeat at home.
Blackpool opened brightly with Ben Burgess winning a lot of aerial ball and the big striker nearly scored with a nicely timed shot from 15 yards out which went narrowly over the bar.
But for all their midfield possession, Blackpool struggled against a well-organised Millwall back four in which Richard Shaw and Neil Harris were outstanding.
Brammer's goal came after 29 minutes when Blackpool gave away a cheap free-kick on the edge of the box.
The home side appeared to have dealt with Neal Ardley's cross easily enough with a big clearing header from Ian Evatt.
However, Evatt's effort came down beautifully to Brammer who was stood 30 yards out and hammered home a wickedly dipping volley.
It was a great goal but it was Brammer's contribution in midfield throughout the game which was even more telling.
He and his colleagues put in some physical but fair challenges on the lightweight Blackpool trio who were far too easily dispossessed or knocked out of their stride.
The Seasiders tried to mount a second half recovery with Grayson sacrificing defenders for substitute attackers.
But Millwall held firm and it wasn't until the 89th minute that Blackpool finally got a shot on target.
Andy Morrell found keeper Lenny Pidgeley off his line and his lovely chip was goalbound until Shaw raced back and scooped the effort off the line.