Mark McGhee is determined to avoid more FA Cup humiliation for Albion.
The Seagulls have suffered a succession of early exits over the past decade.
Embarrassing defeats by Kingstonian, Sudbury and Hereford are still painfully fresh in the memory for supporters.
The new manager wants to ensure his third match in charge, away to Third Division Lincoln on Saturday, does not end in similar disappointment for Albion's 1,100 strong travelling army.
McGhee said: "Every club I've been with I'm sure we have been beaten by lower League opposition, but off the top of my head I tend not to remember my bad experiences!
"The most important thing for me about the FA Cup at this level is that you don't want to lose to a team from a lower division.
"If you come up against a team from your own division then it depends who it is and where it is.
"If you lose to a team from a higher division then normally you have to hold your hand up and say they were better than us.
"Any tie away from home is difficult. If it was Newcastle going to Lincoln on Saturday then people would be saying it's a tricky tie for them, but we have got to be determined not to lose."
The FA Cup has generally been pretty kind to McGhee the manager.
His Millwall side came close to causing an upset in the fourth round last season before losing in a replay after extra time at home to Southampton.
The Lions reached round four the season before as well, going out narrowly to Blackburn at the New Den.
As a First Division club Millwall were, of course, exempt until the third round on each of those occasions.
McGhee's last involvement in the first round was in 2000-2001.
Millwall breezed through a tricky tie away to Leigh RMI, only to come unstuck at Wycombe in a second round replay.
"The best I have ever done was with Wolves, when we went to the semi-finals," said McGhee.
"Like the final at Cardiff, a semi-final was amazing. We played Arsenal.
"If you end up playing a bigger club it's fantastic for boys who have maybe never played at some of these grounds and for the supporters.
"That is what you are really trying to do, to give them the opportunity to go to Man United or Newcastle or somewhere like that."
Albion's record since reaching the final 20 years ago has been pretty miserable.
Steve Coppell's team were unable to take advantage of their third round exemption last season, when they were beaten at Norwich.
The previous season, under Peter Taylor, they reached round three via home wins over Shrewsbury and Rushden and Diamonds, but Preston were too good for them at Withdean.
It is ten years since Albion made a meaningful impact in the FA Cup.
That was under Barry Lloyd, when they lost 1-0 in a moneyspinning fourth round tie at Old Trafford.
Lloyd will be at Sincil Bank on Saturday, working as a summariser for BBC Southern Counties Radio.
Lincoln are sure to make life difficult for the Seagulls, just as their near neighbours Boston did in the LDV Vans Trophy on Tuesday.
The object of the exercise as far as McGhee is concerned is to be in the second round draw, which is made on Sunday afternoon following the Beeb's live game between Accrington Stanley and Huddersfield.
Albion will know their opponents in the southern section quarter-finals of the LDV Vans Trophy before they kick-off at Lincoln.
The draw is on Sky's Soccer AM programme on Saturday morning.
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules hereComments are closed on this article