The Foxes boss will be without nine players for Thursday’s home game due to coronavirus-related issues and injuries.
Seven first-team players, including Jannik Vestergaard, Hamza Choudhury, Kelechi Iheanacho, Ayoze Perez and Ademola Lookman, missed both Sunday’s 4-0 win over Newcastle and the Europa League defeat at Napoli three days earlier.
Leicester’s list of absentees has increased after central defenders Jonny Evans and Caglar Soyuncu both suffered hamstring problems at the weekend.
“We have looked at it,” Rodgers said about getting the match postponed.
“But unfortunately for us we weren’t granted dispensation, which is disappointing because as a team and a club we have always wanted to support all the measures, but when we need a little support with the extreme situation we find ourselves in we weren’t able to get it.
“There was a big doubt for the game against Newcastle, but for the greater good of the game and for the supporters it went ahead. But since then we have picked up more injuries.
“They are not Covid-related injuries, but they are because players are picking up injuries because we can’t rotate the team and the squad because of the number of players we already have out.”
Leicester’s woes could not come at a worse time, with Sunday’s win against Newcastle marking the start of a hectic fixture schedule which sees them play seven matches in 21 days.
“We will put out the best team that we can. We will assess things game by game,” said the Leicester boss.
“If you look at the proximity of the games coming up, it is an incredible run of games and a challenging fixture list at any time when you have a full squad. But with the numbers we have it is extremely challenging. We’ll try to get through it.”
The Premier League’s 2021-22 handbook says matches should go ahead if a club have 14 or more players available on their squad list, but decisions can be taken on a game-by-game basis by the Premier League board.
The PA news agency understands there is no official threshold for the number of positive cases that would cause a game to be called off.
Last week, Tottenham reported eight players and five members of staff had tested positive for coronavirus, leading to their Europa Conference League match against Rennes and Sunday’s Premier League trip to Brighton both being called off.
Rodgers said: “It would be nice if there was a bit more clarity around the issue.
“Games have been called off with less players than we have unavailable. It’s all a bit disappointing, but we have always tried to respect the competition and again that is what we will do.
“There will be opportunities for some of our younger players to be involved and experience the Premier League and that will help their development.”
Daniel Amartey will be back in the squad against Tottenham after initially being one of the seven to miss the games against Napoli and Newcastle.