Jurgen Klopp admitted he "felt alone" as he watched fans leave early in Liverpool's 2-1 defeat at home to Crystal Palace.
Alan Pardew's side earned their third consecutive victory over the Reds thanks to goals in either half from Yannick Bolasie and - in the 82nd minute - lifelong Liverpool fan Scott Dann.
More from FoxSports
Fans streamed towards the exit in the closing stages but Klopp - who tasted his first defeat as Anfield boss - thrust the responsibility on to his players to fight to the end - and instill greater belief in the supporters.
"Eighty-two minutes - game over," said the German, who, after his first game at home against Southampton last month, said his team played like they could not change the outcome after the visitors' 84th-minute equalizer.
"I turned around and I felt pretty alone at this moment but I am not disappointed about this [fans leaving] - they have reasons.
"But we are responsible that nobody can leave the stadium a minute before the last whistle because everything can happen.
"Between 82 and 94 [minutes] you can make eight goals, if you want, but you have to work for it.
"That is what we have to show and we didn't, and things are like they are. We decide when it is over."
Speaking earlier to Sky Sports, the German felt a promising display had been sullied by lapses and urged his players to take responsibility.
"We made a bad start, 1-0 to Crystal Palace because of our start," Klopp toldSky Sports.
"It was not good but after that, we played 75 minutes of very good moves.
"I saw a lot of good things tonight but in the end, we lost. We lost because we lost concentration from a specific point on.
"I feel bad because it was absolutely not necessary to lose. We had all we needed to win.
"If we did the right things in this game, then it would have been a very important game. We didn't show all we could tonight and that's why we lost.
"We are responsible. If you can be better, you have to be better. If you can win, then you have to win. That's how football works.
"We are here to work hard and we have 10 days until we can start again, with Manchester City our next opponent."
The defeat ended a run of 12 games unbeaten for Liverpool in all competitions but though it was the fourth game following a Europa League tie that the club has failed to win, Klopp refused to blame a midweek trip to Rubin Kazan that only saw his side return in the early hours of Friday morning.
"Between the good game against Rubin Kazan and today there was only one thing to talk about - is it too much playing?" he added.
"Once again I decide if I am tired, nobody else. If everyone thinks we gave everything we had then it is wrong. Of course we could do more."