The 41-year-old saw his side's winless Championship run stretched to eight games courtesy of a 2-1 defeat at home to Middlesbrough this afternoon.
Despite the loss, former Liverpool defender Hyypia was defiant and vowed not to quit.
"I'm ambitious and want to be successful," he told Sky Sports.
"I'm willing and I'm not a quitter. I'm a fighter and I hope our team is full of fighters."
Hyypia took the reins at Brighton in June after leaving Bayer Leverksuen, where he spent two years as first-team manager.