The Lions claimed a third Premier League cup scalp this season by beating Leicester City 1-0 at The Den to reach the quarter-finals.
Millwall will play Tottenham at White Hart Lane in the next round, but Harris' focus remains on the league.
"We're at home to Chesterfield on Tuesday night - and if anything that has become more important," he said.
Millwall are on a 10-match unbeaten run in League One and are seventh in the table, outside the play-off positions on goal difference only, with a game in hand.
The south London club will move into the top six if their result against Chesterfield betters that of Southend away at Peterborough.
Harris' side finished fourth last season, before losing to Barnsley in the play-off final at Wembley, and the former Lions player is hoping to go one better this season.
The 38-year-old told BBC Radio London: "My achievement this year is promotion - that's what I want to be judged on.
"We want to get out of this division. We started the season looking to consolidate a play-off position.
"We overachieved last year with spirit and determination. We had a slow start this year, but we've got ourselves into a good position."

The lyrics are from Vegas, a track on Eminem's upcoming compilation album.
He raps: "So what's it gon' be? Put that away Iggy. You don't wanna blow that rape whistle on me. Scream!"
Azalea also said that she is "bored of the old men threatening young women as entertainment".
She said that women in the music industry have "bigger balls" and "endure much more harassment".
Of course Eminem is famed for his controversial lyrics.
In a freestyle rap to promote his new album he said he would "punch" Lana Del Ray.
He also referenced the shocking case of an NFL footballer who in September was seen in video footage attacking his wife in a lift.
"I'll punch Lana Del Rey right in the face twice," he raps, "like Ray Rice in broad daylight".
"The new Eminem rap song is yet another example of a stream of music videos that glamorises and normalises rape, rape culture and violence against women," Betiel Barakia, a spokesperson for Object, which tackles issues around women and girls in the media, told Newsbeat.
"It normalises and legitimises forms of behaviour that should be condemned, not celebrated or tolerated.
"Eminem is a global, successful rapper; his target audience are young boys and he, alongside the music industry as a whole, have a responsibility towards their audience."
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Millwall boss Neil Harris believes promotion from League One is "more important" than FA Cup success.
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Iggy Azalea tweeted that her younger brother is "the biggest Eminem fan and now the artist he most admired says he wants to rape me."