The England international missed a penalty, generously handed to him by captain Steven Gerrard, which would have completed his treble and then later found himself so focused on trying to score he completely ignored his strike partner in a much better position in front of goal.
That prompted a good few minutes of verbal complaint from the visibly unhappy Uruguay international before Sturridge was substituted by manager Brendan Rodgers, which provoked a mild show of petulance from the 24-year-old.
Sturridge apologised to his team-mates in the dressing room and was instantly forgiven and he believes that team ethic will stand them in good stead as they seek to secure a top-four spot.
"Luis was obviously fuming - I think everyone was fuming with me and I was fuming with myself," said the England forward, whose two goals against Everton took his tally to 15 for the season.
"You could see I was disappointed with missing a penalty at the Kop end but it was more important we won the game and everyone was happy.
"I am disappointed not to score a hat-trick but at the same time we won 4-0 at home against Everton and I can't be too hard on myself.
"Somtimes you score, sometimes you get a hat-trick, sometimes you don't and it wasn't the night for me.
"But it was fantastic for the boys and for the fans.
"We wanted to put on a performance and work hard as a team and we are delighted with the victory.
"It is about the team. I keep saying it but it is about the boys working hard as a team and if we do that we will get results.
"The boys give me the licence to do what I do, we work tirelessly as a unit and that is what it is all about - just being out there as a team and enjoying every moment as a team.
"There are 15 games to go and we'll take every game as it comes and work hard as a team and see where we are at the end of the season."
Sturridge has been at the club just over a year, having proved to be a January transfer window success with 26 goals in 32 appearances.
He has forged a devastating partnership with Suarez, with the pair contributing 36 league goals in the current campaign, and is enjoying his football.
"The love I have for this club grows each day and I want to thank the fans for the way they have embraced me," he added.