Having been beaten by Manchester United before the international break, Liverpool slipped to a second successive league defeat to one of their closest rivals, as three goals in eight minutes before half-time effectively gave Arsenal the points.
That blitz came after Liverpool had missed multiple chances and, although Henderson pulled one back from the penalty spot in the second half, Arsenal cruised home, adding a late fourth through Olivier Giroud after Emre Can had been sent off.
The Merseyside club now sit seven points adrift of the top four with as many games remaining, leaving their UEFA Champions League ambitions hanging by a thread - although Henderson is not about to accept they are out of the race.
"To concede three goals in such a short space of time is not good enough," the England midfielder told Liverpool's official website. "Our one-v-one defending needs to be better.
"I'm sure we'll work on that in training. We've just got to be a little bit more aggressive defensively, and then also in the final third be more ruthless.
"We knew it was going to be difficult [to finish in the top four] even before we came here, but it makes it even more difficult.
"That doesn't mean we'll just give up. We've got seven games left now and we need to try and win every one. If we do that, then you never know."
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