The Seagulls host the Tigers in what promises to be a wide open fifth-round tie at the Amex Stadium, with a place in the quarter-finals the prize for the victors.
Heading into the eight fifth-round fixtures, Albion were one of six teams still remaining in the competition from outside the top flight, with at least three of those guaranteed to progress.
Current holders Wigan disposed of Cardiff 2-1 on Saturday, Sky Bet Championship rivals Sheffield Wednesday and Charlton will go again after their tie was postponed while League One Sheffield United host Nottingham Forest on Sunday.
But Garcia is not getting distracted by the potential prospect of a favourable FA Cup run.
"I am only focused on our draw and our game, not the others," said the Spaniard.
Indeed, Brighton will already know their possible quarter-final opponents before the meeting against Hull, with the draw for the last eight due to be made on Sunday afternoon.
Asked whether a potential tie against a cup favourite or relative minnow changes his thinking, Garcia simply replied: "No."
Albion head into their meeting with Hull currently on the periphery of the play-off places in the Championship but firmly chasing a top-six finish to replicate their achievements of last season.
The two sides shared a narrow 1-0 win apiece during their encounters last term before Hull claimed promotion to the Barclays Premier League, where they currently sit 13th - three points off the relegation zone amid a congested battle for survival.
Casting an eye over his opponents, Garcia said: "They are in a comfortable position (in the league), they are always well organised and they don't concede many goals.
"But we need to enjoy the occasion, playing against Premier League opposition."
He added: "We always want to play in front of our own fans, it will be a great atmosphere under the lights.
"Everyone needs to enjoy the occasion, playing against Hull, enjoy the game and we will see what happens."
Monday's clash will be broadcast live on television, ensuring the Seagulls are on show as they reach out to a much wider audience.
But Garcia hopes that does not make any difference to how his players approach the tie.
"Whether games are on television or not, we can't change how we play or our mentality," he added.
"It would not be good when we play on television if we play with more intensity and energy, I want to play all games like how we are playing and not focus if we are on television or not."
Will Buckley is set to make his first start of 2014 having overcome a hamstring injury to return to action as a second-half substitute against Leeds on Tuesday.
Midfielder Keith Andrews (hamstring) is expected to be fit while right-back Bruno (thigh) will be assessed as Brighton chase a fifth successive home win.
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