The Reds somehow found themselves level at half-time despite not having had a shot on target, a Gabriel own goal in stoppage time cancelling out Bukayo Saka's opener.
Just as Liverpool looked to have taken it up a gear after the restart, Jurgen Klopp's side shot themselves in the foot once again, an almighty mix-up allowing Gabriel Martinelli an open goal to put the Gunners ahead.
A long and aimless ball over the top was left by captain Virgil van Dijk as Alisson rushed out of the Liverpool goal to clear, but both players missed the ball entirely as Arsenal's Brazilian forward snuck in for the easiest goal of his career.
It was a disastrous moment for the Liverpool backline in a game of great significance, with former Red Owen and ex-Arsenal striker Wright blaming Alisson for the goal that restored the hosts' lead at the Emirates Stadium.
"Listen, you can blame both of them in many ways. I think, potentially, Virgil van Dijk could head this one. He could head it and he lets it bounce.
"After that, he is in total control if Alisson stays on his line. He is in control. He is happy one-v-one. Stronger and quicker. He’s goal side and absolutely in control, just don’t come out and leave him to it, then Alisson comes out and actually half collides and none of them touch it – so, I think it’s more Alisson’s fault than Van Dijk’s."
On that goal, Wright added: "If Alisson doesn’t come, then there is Gabriel Martinelli and there is no way he gets on that side of Virgil. No way he is getting on that side – but seeing Alisson there and getting the little nudge, it’s confused everything. He needed more communication from the goalkeeper."
Alisson and Van Dijk weren't interested in divvying up blame after the goal went in, with both players hardly covering themselves in glory for Arsenl's second.
The pair were also unimpressive for Arsenal's third, while Van Dijk's decision to rush into midfield for Saka's opener proved costly.
It was a disjointed defensive display from the Reds but the general performance from front to back was seriously underwhelming.
The Reds will have to restore some of the damage when Burnley visit Anfield in the Premier League next weekend.