Brendan Rodgers admitted that he was not immune from the sack after Liverpool slumped to a demoralising 3-1 defeat to Crystal Palace and he called for an immediate improvement from his side in Wednesday’s crucial Champions League match against Ludogorets.

Although Rodgers did not spare his players from criticism after a fourth successive defeat in all competitions, accusing them of failing to show enough intensity or togetherness against a Palace side who had not won since the end of September, he accepted that the responsibility for Liverpool’s poor form ultimately lay with him. This latest setback leaves them 12th in the table, five points behind fourth-placed Manchester United, and Rodgers did not shy away from answering questions about his future.

“I’m not arrogant enough to think that I will be in a job through anything,” Rodgers said. “Any manager will tell you that you have to win games and you have to get results, especially after how we’ve been developing as a football club. But I have a great communication line with the owners. We’ve been honest enough with each other but ultimately you have to get results. You have to perform. In my first year when we weren’t maybe getting the results we were performing well.

“Owners and directors and chairmen and chief executives have to see development on the field. Barring this period, our development has been very good and fast. But there’s no doubt as a manager you have to get results. That will support the confidence to the owners, and you take it from there. I will only ever do my best. The best has seen us develop well. Now I need to fight even harder. And take the responsibility because as manager full responsibility comes down to me. Any pressure comes on to me.”

Liverpool visit Ludogorets needing a win against the Bulgarian club to keep alive their hopes of qualifying from their Champions League group but they will have to play much better than they did against Palace. Rodgers said that Liverpool were guilty of not managing the game properly, although he must have thought that everything was going to plan when Rickie Lambert gave them the lead after two minutes with his first goal for the club since joining from Southampton.

Yet instead Rodgers found himself talking about his side’s lack of confidence after Palace fought back to claim their first win in six matches thanks to goals from Dwight Gayle, Joe Ledley and Mile Jedinak.

“It was bitterly disappointing,” Rodgers said. “Nowhere near the levels we’d expect, after a very good start. You’ve seen a team low on confidence today. Not quite together as a team. We need to find a solution very quickly because it was very disappointing.

“It’s my responsibility as the manager, ultimately. I put the team out there, the best team to win us the game. We made a good start. You could see our passing was a wee bit tentative, and then we make mistakes. Mistakes you wouldn’t expect to see from a team that’s supposed to be challenging. We failed to manage the game.

“We concede a throw-in which shouldn’t happen and then the third goal, a long ball down the middle and I didn’t think it was a free-kick. Both were holding each other’s shirts. OK, it was a good free-kick. Overall, that intensity and togetherness in our game isn’t there.

“When you don’t get the results, that affects you. We have to work harder but we go away bitterly disappointed with the result. We have to put it right very quickly because we have a massive game in midweek and a busy schedule ahead. We have to do better.”

Rodgers said that there was no issue over Mario Balotelli, who was absent with a groin injury, attending Saturday night’s fight between Tony Bellew and Nathan Cleverly in Liverpool but added that he was unsure whether the striker would be available against Ludogorets. Liverpool are without Daniel Sturridge, who is now out until the new year with a thigh injury.

“Mario came back from the Italian squad and the groin was still sore,” he said. “We’ll assess that over the next few days. He was obviously free. He wasn’t out too late and he was in for treatment today.”