Ahead of the encounter at the Emirates, only six points separated the hosts in third from the Reds in fifth, with Manchester United sandwiched in-between.
The Red Devils triumphed at Anfield 2-1 two weeks ago and subsequently put distance between themselves and the Reds, making today’s clash at the very least a must-not lose encounter for the visitors.
However, goals from Hector Bellerin, Mesut Ozil, Alexis Sanchez and finally Olivier Giroud handed Arsene Wenger’s men a huge victory and a nine-point advantage over their opponents.
Following United’s straightforward 3-1 home victory over Aston Villa, the Merseysiders are eight points adrift of the top four with only seven games remaining – a gap Keown feels is now too big to bridge.
“What this was about from an Arsenal point of view was taking Liverpool out of contention for a Champions League place,” the BBC pundit explained.
"It will take a lot for Liverpool to bounce back from this today. Arsenal were well ahead of them today.”
With just 21 points left to play for, Brendan Rodgers’ men will arguably have to win all of their remaining fixtures to stand any chance of making the top four.
Difficult trips to Chelsea and Stoke City still await, though United boss Louis van Gaal told the BBC that it’s not yet a foregone conclusion regarding what he labels ‘a rat race’.
"We are still not certain about Champions League qualification - it is still a rat race,” the Dutchman conceded.
"But we have given a blow to Liverpool and Southampton also lost. It is a big gap. Now we have to wait to see if the gap is too big for Tottenham too. But we have to play the top three - it is still a rat race."