Fulham manager Claudio Ranieri said his side are "alive and will continue to fight" despite losing to Tottenham through Harry Winks' injury-time header at Craven Cottage.
Spurs, who had already lost Dele Alli to a hamstring injury, looked set to concede further ground on league leaders Liverpool but Winks stooped low in the 93rd minute to head past Sergio Rico from close range.
"It was a bad moment for us," said Ranieri, whose side are 19th and seven points from safety.
"The performance was fantastic, but we lost the match through experience, that's it. At the end we took a free-kick into the box. Why? We should have taken the ball into the corner.
"We played well and sooner or later we will find our way. We have to continue to believe. Now we have to stay together and I hope other players arrive to help us."
Winks' last-gasp winner means third-placed Spurs have a seven-point cushion over Arsenal in fifth in the battle for Champions League places.
"Sometimes in football, it is not tactics or formation - you have to believe," said manager Mauricio Pochettino.
"It was an unbelievable finish. That's why it is so important to believe."
Fulham had nine shots on goal in an impressive first half and took a deserved lead when Tottenham striker Fernando Llorente scored an own goal.
The Spaniard, making his first Premier League start of the season in place of the injured Harry Kane, inadvertently beat Hugo Lloris from close range while attempting to clear the danger inside his own six-yard box after a Jean Michael Seri corner.
The hosts thought they had doubled their lead five minutes before the interval but Aleksandar Mitrovic's header was ruled out as the Serbian was adjudged to be offside.
However, Spurs responded in the second period and they drew level six minutes after the interval when Dele Alli ghosted in behind the Fulham defence to head a pin-point Christian Eriksen cross past Rico.
And Winks completed the turnaround in stoppage time when he met substitute Georges-Kevin Nkoudou's cross to break Fulham's resistance.
The 50th meeting between these two London clubs saw Tottenham - the side with the best away record in the league - facing the division's worst defence.
However, Spurs were without their two top goalscorers because of injury (Kane) and international commitments (Son Heung-min), and for 50 minutes, they looked devoid of ideas and opportunities to break down their well-organised opposition.
Pochettino's men had just four shots in the first half, which was less than half the number Fulham produced (nine).
The man chosen to play instead of talisman Kane made an impact at the wrong end and Son's replacement, Erik Lamela, only managed one shot at goal in the 79 minutes he was on the field.
Spurs were better after the break as Eriksen's influence on the game began to grow, but when Llorente had a late chance to make amends for his earlier mistake, his header drifted wide with the game heading for a draw.
'Sometimes football is about belief' - Pochettino on Winks' late winner BBC Radio 5 live pundit Jermaine Jenas said: "It's a big, big moment in Spurs' season. Everything was negative with regards to the players missing but they kept plugging away, they kept getting the ball into the box and it was one of their own in Harry Winks who saved the day today.
"They've got a lot of players to patch up and get out there for the next game but that will feel huge."
Fulham's debutant winger Ryan Babel looked like he enjoyed his first Premier League start since December 2010, after completing a move from Turkish side Besiktas earlier this week.
The former Liverpool forward showed plenty of encouraging signs for the hosts and he should have scored in the 11th minute when he burst clear of Davinson Sanchez with pace and power, but his left-footed effort was well saved by Lloris.
He then came close to doubling Fulham's lead while they were in the ascendancy, but his header sailed over the bar after he rose highest to meet Cyrus Christie's cross.
Babel last played for Besiktas on 22 December and he was replaced after 50 minutes, but the 32-year-old had more shots and played more key passes than any other Fulham player during the whole game.
The Netherlands international gives Claudio Ranieri's side an option they have not had so far.
Spurs boss Mauricio Pochettino to BBC Sport: "The action is brilliant from Harry Winks, to recover the ball from a difficult position, he believes to score and arrive in the box. It was an amazing cross from Nkoudou.
"Some injuries appear in a period with a more busy schedule and another opportunity opens the door for players not consistently in the starting XI or on the bench. It is great opportunity for different players to show quality."
On Alli's injury: "It is in the left hamstring, I hope it is not a massive problem, but we will need to assess."
"Unbelievable. Our first half was fantastic and we also had a penalty the referee didn't see. There was a big penalty on Mitrovic.
"Second half we controlled the match very well in different ways. We gave a gift with the first goal and the second goal is unbelievable.
"We lack experience. Calm, stay calm, keep possession, finish the match."
On Ryan Babel's debut: "He had a fantastic first half but has come from a winter break so I think in one month he will be ready for 90 minutes."
