Boss Nigel Pearson insisted he will not "stick his head in the sand" after Leicester fell six points adrift of the safety line.
But the Foxes chief praised his side's performance despite their 2-1 defeat to Tottenham keeping them bottom of the Barclays Premier League.
Harry Kane's first-minute strike and Christian Eriksen's free-kick squeezed Spurs to a win at the King Power Stadium.
Leonardo Ulloa equalised and Leicester's performance deserved better but Pearson admitted they need points after 13 winless games.
"I'm not sticking my head in the sand and trying to paint a more positive picture - we're in trouble but the performances suggest we have the capability of turning things around," he said, ahead of Sunday's trip to Hull, who are 17th in the table.
"It does test your resolve but that's how it is and we will need it.
"We should do better in defence. It remains very frustrating for us. We were by far the better side in the second half but were not able to make the most of our advantage.
"I don't like playing the bad luck card. We are close to making things happen. We need to push our performance levels to make things happen."
Ulloa scored his seventh goal of the season and also hit the post from a free header during a spell of domination from the Foxes.
Wes Morgan missed a golden chance to level in the final minute and Pearson revealed his frustration after they did not get their rewards.
"We're still not getting the results. That in a way is even more frustrating. They did really well," he said.
"They've had a number of performances of late where they have not got the results so it will be a test of their resolve as much as possible.
"I've been very proud of how they have gone about it. I should be talking about a win not a defeat and that's even more galling.
"You need to do something about it and we will continue.
"We will need to try and win our game and see how things develop."
Victory left Spurs a point adrift of the top five and Kane now has 15 goals this season with Eriken on seven.
Boss Mauricio Pochettino said: "I am happy for them and I am happy for the team. It was a very good result.
"The reason they both keep scoring is they always try to get into scoring positions and they have the desire to score.
"It is not one of those things - they train hard for this.
"They both keep wanting to score.
"Christian has a free role. I think he is a player you need to give confidence."
And the head coach eased fears over Hugo Lloris after the goalkeeper was left with a bloodied mouth following a collision with Jamie Vardy.
He added: "He was only cut inside his mouth. It was not like last time (when the goalkeeper suffered concussion against Everton last season).
"He will not need clearance to play against Manchester United (on Sunday). This was nothing like before.
"From my position it was difficult to see the incident but it is not serious and he will play. He is very brave."