Manager Claudio Ranieri, who scored a massive new contract after winning the EPL, lost his cool in the previous draw against Stoke City, remonstrating with officials at halftime after Vardy had been sent off.
Sky Sports pundit Jamie Carragher, who played more than 500 games for Liverpool, expressed his fears for Leicester early this month after a defeat to Sunderland.
"The situation at Leicester is becoming alarming," he said. "The more you look at it, the more you think they will be involved in a relegation scrap.
"We all expected Leicester to drop off, what they did last season was unbelievable and we'll be talking about it for years - the players will always be remembered for that.
"You don't want the Leicester fairytale story turning into one of the champions being relegated. It may take something away from their title win and lead to it being labelled as a fluke, almost like they didn't deserve to win it, which they did.
"I don't think they will get relegated, but something has to change quickly."
After the Everton defeat, the BBC reported that: "Leicester's remarkable Premier League title success last season was underpinned by their defensive fortitude, but sloppy errors are costing them this term.
"It was also another reminder for Leicester's players and fans of how unforgiving the Premier League can be."
Meanwhile Boxing Day brought a vital win for Winston Reid's West Ham - the All Whites captain scored with a header in the 4 - 1 away win over Swansea. It was West Ham's third straight win, lifting them into a mid table position.