Although decorum and a rarely shown respect for the old ways means it is not publicly permitted, behind closed doors, few Premier League teams care for the FA Cup.

The riches available for remaining in the top flight are the only priority for many and that thought now permeates English football like few others.

Yet, every season, the Third Round of the FA Cup comes to the rescue of at least one Premier League side. It acts like a First Aid station, where beleaguered managers and their beleaguered players can get their morale and confidence patched up before they head out for the second half of a beleaguered season.

Twelve months ago, when Leicester City were knocked out at this stage of the competition, few tears were shed at the King Power Stadium.

After all, loftier ambitions were at stake then. This time last year, Leicester were second in the Premier League with 11 victories and 40 points as their season mirabilis started to take shape.

On Saturday, they were 15th with just 21 points and a battle against relegation seems likely. In other words, the FA Cup came at the perfect moment. And how they seized that moment might come to shape the remainder of this term.

Although Romelu Lukaku finally offered a bright moment in this hitherto sluggish match with an easy close-range finish following Gerard Deulofeu’s slide-rule cross after 63 minutes, two quick-fire finishes from Ahmed Musa, carving Everton open twice in the space of five minutes, placed Claudio Ranieri’s men in the Fourth Round.

Leicester City Premier League title celebrations Show all 10 1 /10 Leicester City Premier League title celebrations Leicester City Premier League title celebrations Leicester City supporters celebrate within the Market Tavern after the English Premier League soccer match between Chelsea and Tottenham Hotspur EPA Leicester City Premier League title celebrations Leicester City fans celebrate their team becoming the English Premier League champions in central Leicester Getty Images Leicester City Premier League title celebrations Leicester City fans celebrate outside the King Power stadium Reuters Leicester City Premier League title celebrations Leicester City fans celebrate outside the King Power stadium Reuters Leicester City Premier League title celebrations Leicester City supporters celebrate at the Haymarket Memorial Clock Tower EPA Leicester City Premier League title celebrations A Leicester City fan stands on top of an advertising board near the clock tower in Leicester after seeing their side crowned Barclays Premier League champions following Tottenham Hotspur's 2-2 draw against Chelsea PA Leicester City Premier League title celebrations Leicester City fans celebrate their team becoming the English Premier League champions in central Leicester Getty Images Leicester City Premier League title celebrations Leicester City supporters celebrate at Haymarket Memorial Clock Tower EPA Leicester City Premier League title celebrations Leicester City supporters celebrate near the Haymarket Memorial Clock Tower EPA Leicester City Premier League title celebrations Leicester City supporters celebrate after the English Premier League soccer match between Chelsea and Tottenham Hotspur EPA

Short of Riyad Mahrez, Jamie Vardy, Islam Slimani and Andy King, Leicester showed most of the battling qualities that took them to the title last season and the size of the confidence boost they will receive for the Goodison Park exploits is expected to be vast.

“So many times I’ve said ‘Hey, I’ve got some very good players and a very good squad’,” Ranieri said, about the way his supposed second string played on Merseyside.

“But of course when things don’t go well people ask what happened? Nothing - just wait for the right moment. And now I hope this is the right moment to go back [up the table].”

Particular praise was heaped on Musa - a summer signing from CSKA Moscow who was a first half substitute for Leonardo Ulloa - as well as Wilfred Ndidi, another African youngster who looked every inch a superb N’Golo Kante impersonator on his Leicester debut.

“It’s important Musa keeps going to maintain this momentum and the last month I saw him go well in training sessions and today he scored two goals and I hope now that he’s getting better and more confident,” Ranieri said.

“I love players who recover the ball and pass the ball straightaway forward,” the Leicester manager said of Ndidi. “For the first time, at 20 years old against Everton - one of the bigger teams in the Premier League - he played fantastic and very well.”

As for Everton, this really was a hammer blow. Their early season optimism has evaporated and in the first week of the new year they are out of all competitions and face a long struggle to convince their supporters that happier times are ahead.

Manager Ronald Koeman was an almost caricature-like example of suppressed rage after this match - not for the first time this season - and he again spoke of the need for Everton to reinforce his side in this month’s transfer window.

“For the rest of the season it’s easy - to try to keep this position in the table because there is a big difference between the first six and the rest of the teams,” he said.