Rodgers said at his pre-game press conference on Wednesday that he would be without nine players due to positive cases of Covid, illness and injury.
Tottenham’s last two games, against Rennes in the Europa Conference League and Brighton in the Premier League, have been canceled due to an outbreak that saw at least eight players and five staff test positive.
The trip from Manchester United to Brentford planned for Tuesday has also been postponed due to several cases in the United camp.
“We looked at this, but unfortunately we weren’t given a waiver,” Rodgers said.
“As a team and club, we have always wanted to support all measures, but if we need a little support in the extreme situation we are in, we have not made it.”
Leicester lost seven players in their 3-2 loss to Napoli last week.
Rodgers said the weekend’s additional absenteeism were more injury-related than more coronavirus cases.
However, the Northern Irishman believes the injuries were caused by fatigue as his squad was stretched due to the Covid outbreak.
“There were big doubts about Sunday’s game against Newcastle but it went on for the good of the game and for the fans,” added Rodgers.
“We’ve taken more injuries since then. They have nothing to do with Covid, but they are because players get injured, because we can’t change teams and squads because of the number of players we already have.”
Rodgers has joined a growing group of Premier League managers seeking clarity on how many positive cases it will take for a game to be postponed.
The Premier League has so far accepted or rejected requests for postponement on a case-by-case basis.
Tottenham are struggling to fall behind as their last Premier League game before the Burnley breakout was also postponed due to bad weather.
Spurs boss Antonio Conte said he would also have preferred to postpone the game, but believes the possible buildup of games is behind the Premier League’s deliberations.
“The Premier League didn’t want to postpone the game against Leicester,” said the Italian. “Maybe because we have to play Burnley and Brighton and had previously postponed two games.”
Conte will be making some of his players who tested positive again for selection at King Power, but said he will not be able to start them due to the effects of the virus and self-isolation on their fitness.
“(Some) players are back in training and other players continue to be isolated. For the players who are back in training, they need some time to get fit and get back into good physical shape,” added Conte.
“If you don’t have Covid for just 10 days, you don’t make your body so strong with this virus. For this reason, you have to proceed slowly.”
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