Vardy, 29, is serving a three-match ban after being sent off at Stoke on 17 December for a two-footed challenge on Mame Biram Diouf.
The Foxes had 30,000 masks printed after Vardy had an appeal rejected by the Football Association.
Vardy sat in the stands and wore one of the masks himself.
The England international will also miss games against West Ham and Middlesbrough but will be available for the FA Cup third-round tie against Everton at Goodison Park on 7 January.
Leicester boss Claudio Ranieri said he did not emerge from the tunnel at the King Power Stadium in time to see the masks.
"I'm sorry, I didn't see when I came out. I don't know, it's not my matter. I didn't see. I'm sorry," he said.
"It's difficult to say how much we missed Vardy. I didn't see the masks."
In an Instagram post, Foxes owner Vichai Srivaddhanaprabha said the decision to suspend Vardy was "unfair".
Leicester forward Riyad Mahrez was left on the bench against Everton by Ranieri and the Foxes boss has demanded an improvement from the Algerian.
"He's not in good form now and I wanted to stimulate him," said the Italian.
"I didn't see him do well during the training sessions and he must give more for the team. I want more."
The Premier League champions have won only four of their opening 18 league games and are three points above the relegation zone.
"This season is this way - nothing is right, nothing is easy," added Ranieri.
"We wanted to give a good present on Boxing Day, but it was not possible. Here everything was right in first six months and now everything is wrong."
Leicester City fans wore Jamie Vardy face masks for their 2-0 defeat by Everton on Boxing Day to show their support for the suspended striker.