Two goals from Aaron Connolly and one for Neal Maupay did the damage for the hosts, with a serious injury to Hugo Lloris adding to Spurs' dismay.
They have also lost 17 times in all competitions in 2019 - more than any other top-flight side in the same calendar year - to pile the pressure on manager Mauricio Pochettino.
"As a group though, it’s fallen apart. Something’s going to have to change," former Spurs midfielder Jenas told BT Sport .
"I’ve been at that club when there’s been changes. I love Mauricio and I hope he stays.
"It stinks of that type of moment. Things seem very stale. He’s been there a number of years.
"The club have let Mauricio down. Something needs to change. Hopefully it’s the players’ mentality rather than the manager."
Former Chelsea midfielder Joe Cole believes the north Londoners were "tactically inept" during the 3-0 defeat to Brighton and suggested that it could well be difficult to Pochettino to remain in the job.
He said: "The club’s in disarray. We have to credit Brighton, but today Tottenham were dreadful. No desire, no heart. There was no press. Tactically they looked inept.
"They looked disinterested on the bench. I think we’re getting to the point where it’s the end of the road for this team.
"And the manager – it’s going to be difficult. He’s an asset to the club. It’s not like a normal situation where you can let the manager go and let someone else in."
Spurs face the league’s bottom side Watford when the Premier League resumes following the international break, and already face an uphill struggle to qualify for next season’s Champions League.