But they were back in contention after 56 minutes - and it was Sanchez who created the goal.
Speaking to talkSPORT host Jim White, Murphy said: "Brendan Rodgers was one game, you could argue one slip, away from winning the Premier League, from being the legend and maybe even being still in the job now".
"Arsenal are a good football-playing side and we need to bounce back". It was the awful start to 2017 that saw them drop to fifth place with just one point more than sixth-placed Manchester United.
Victory, however, would take Liverpool above the north Londoners, and keeper Simon Mignolet believes the visit of Arsenal could help them get their season back on track.
Arsenal continued to press as the game entered its final moments, but after Alexis Sanchez had seen a late effort blocked by Matip Liverpool swept to the other end and Georginio Wijnaldum finished a lightning counter-attack involving Adam Lallan and Origi to crown an impressive evening's work.
Sanchez - a pivotal contributor to the visiting side's second half revival, according to Liverpool manager Jurgen Klopp after the game - was clearly deeply unhappy to be on the bench but Wenger insisted that it was justifiable.
Arsene Wenger looked at his away trip to Liverpool, where there was a top four spot on the line.
Liverpool-Arsenal meetings normally provide plenty of goals, too-there's only been one 0-0 league draw between the clubs since the turn of the decade, and the reverse fixture finished 4-3. The Reds are unbeaten against the top six sides this season, but they have seriously struggled against the minnows.
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Arsenal haven't won any of their last 11 Premier League away games against the other teams now in the top six (W0 D5 L6). He was sitting when Roberto Firmino scored after nine minutes.
Skipper Jordan Henderson is set to miss a second consecutive game with a foot problem, while Daniel Sturridge, after missing out through illness last time, will now sit out with a minor hip injury.
Philippe Coutinho is a huge player for Liverpool - his header in the build-up to Firmino's opener was majestic and his movement had Arsenal chasing shadows all night.
If Liverpool play with that energy that is associated with them they will win this game. Substitutes: Alexis Sanchez (for Coquelin, 46) 7, Lucas Perez (for Giroud, 74) 5, Theo Walcott (for Welbeck, 74) 5.
Arsenal are not almost so strong against their closest rivals: their record against the top six reads W1 D2 L3.
The Gunners were torn to shreds in the second first half, giving up a 2-0 lead.
But Arsenal have no such luck. "If they were challenging for the top of the Premier League he would fight it out".
And on Saturday, 11 March they play Lincoln in the FA Cup sixth round.