Jurgen Klopp’s side, who knew that top four rivals Chelsea and Leicester City had dropped points earlier in the day, dominated the game at Arsenal on Saturday night, but were forced to head in level at 0-0 at half time.
Liverpool took the lead in the 64th minute through substitute Diogo Jota, before Mohamed Salah then made it 2-0 four minutes later to leave Arsenal reeling.
Jota then scored again in the 82nd minute as Liverpool cruised to a 3-0 win that leaves them just two points behind fourth placed Chelsea.
Thompson feels the result in no way flatters Liverpool as he stressed the Reds dominated Arsenal and had their rivals slipping up in their thoughts.
“We said the importance of it prior to the game”, Thompson said post match on LFC TV.
“The staff and the players had seen those results, Chelsea and Leicester being beaten, and you go ‘come on boys’.
“The performance was excellent and 3-0 was just about right because of our domination of the game.
“You can go right through to the front lads, absolutely exceptional.”
Liverpool are next in action in Spain against Real Madrid in the Champions League, while their next Premier League assignment comes next Saturday, when Aston Villa visit Anfield.