Thomas Frank said on Monday that Tottenham have to understand the gravity of their predicament to snap a seven-game winless run in the Premier League against Newcastle on Tuesday.
Spurs sit just six points above the relegation zone in 15th.
Frank has so far been handed a stay of execution by the club's board, but did not play down the desperation of his side for just a third home league win of the season.
"There is no doubt we are desperate to win games," said the Dane at his pre-match press conference.
"You need to be desperate. If you are not desperate, you do not understand the situation you are in, in terms of you haven't won enough and you need to win football games.
"That's what we want for the fans, for the team, for the club."
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Frank has faced repeated calls for his head by a frustrated Tottenham support during a miserable first season in charge.
But with his squad ravaged by injury, he called on the supporters to give their side the encouragement they need to dismiss fears of a relegation battle.
"When you are in a situation, when it's not going straightforward, you need the fans more," added Frank. "We need the fans tomorrow, massively, to back the team."
Already short of options, Frank will now be without captain Cristian Romero for four games after he was sent off in a 2-0 defeat to Manchester United on Sunday.
Destiny Udogie also picked up a hamstring injury in that match, which will rule him out for up to five weeks.
Romero has been criticised for picking up the sixth red card of his Tottenham career just days after he spoke out publicly to lambast the club's board for not doing enough to help the squad in the transfer market.
But Frank defended the Argentine international's disciplinary record.
"When you have a player that's playing with so much passion and aggression, things like that can happen," said the former Brentford boss.
"That's not to say he shouldn't learn from it. Of course, he needs learn from it going forward."