According to the BBC, the oft-maligned 23-year-old, who started for the Netherlands in Thursday night's (31 August) heavy World Cup qualifying defeat to France in Paris, rebuffed a prospective loan move to the Amex shortly before the window closed at 23.00 BST despite the two clubs coming to an agreement.
Janssen has struggled badly to replicate his prolific Eredivisie form since arriving in English football from AZ Alkmaar in a £17m ($21.9m) deal last summer, notching only two goals from open play in 39 appearances across all competitions.
His previous position as the chief back-up to leading forward Harry Kane had already been downgraded after Mauricio Pochettino often turning to other options when his reigning Golden Boot winner was out injured last term.
West Bromwich Albion reportedly tabled a permanent £23m offer for Janssen, while Stoke City were also said to hold an interest in his signature. However, Brighton was the only realistic option to materialise late in the day and it appears that the player had no intention of boosting the Seagulls' survival bid.
Addressing his seemingly bleak Spurs future earlier this week, Janssen said: "You're never happy with this [being a back-up option], everyone wants to play, but the situation is so. If I'm staying? I do not want to say too much about it at the moment. I want to focus on the Netherlands, the other questions I leave for later."
With Glenn Murray (ankle) and Sam Baldock (calf) both sidelined and question marks over Tomer Hemed's ability to cut it at the top level, Brighton were desperate to land at least one new striker on deadline day.
Having already wrapped up deals for Sporting Lisbon defender Ezequiel Schelotto and Newcastle United goalkeeper Tim Krul, last season's Championship runners-up, who have yet to score in their opening three Premier League matches, were even granted a two-hour extension to complete the paperwork on a new frontman believed to be Janssen.
However, that signing obviously never came to fruition and a deal for Deportivo La Coruna forward Florin Andone similarly fell through. They also had no joy in pursuit of Fiorentina's Khouma Babacar or Karl Toko Ekambi of Angers.
Brighton chairman Tony Bloom penned an open letter to supporters on Friday morning in which he admitted that the failure to acquire the additional striker that manager Chris Hughton needed in a "highly complex and dynamic" transfer window had left everyone feeling "very disappointed".