Spurs have 'big problems' says Tudor as relegation risk persists
Still without a league win this year, Spurs remain just four points above the relegation zone in 16th with 10 games remaining.
Tudor was taking charge for just the second time since being appointed until the end of the season.
But if the Croatian could excuse last weekend's 4-1 north London derby to Arsenal on the gulf between the sides, he was left with no doubt over the task he faces in the coming months.
"We were not good, (we) lacked everything attacking and defending," said the former Juventus boss.
"Fulham were much better. There are problems here, big problems.
"We need to stay calm, believe in what we are doing in training, and get out (of trouble), staying all together."
Tottenham have been an ever-present in the English top-flight since one season in the second tier in 1977/78.
They are among the top 10 richest clubs in the world based on revenue and boast a state-of-the-art stadium and training ground.
But Tudor said relegation is a realistic possibility unless his side improve markedly in the coming weeks.
"We don't need to think about that (relegation), not because it cannot happen, but we must focus on growing mentality as a team, concentration, physically," he added.
"These are the only goals we must have."
There was frustration for Spurs over the award of Fulham's opening goal.
Harry Wilson fired in after Raul Jimenez pushed Radu Dragusin in the back with a very similar action to one penalised when Tottenham forward Randal Kolo Muani nudged Arsenal's Gabriel Magalhaes last weekend.
"Of course it's a foul," said Tudor. "It's an incredible mistake."