Eight players have withdrawn from the latest squad, with Aaron Ramsdale, Trent Alexander-Arnold, Levi Colwill, Declan Rice, Bukayo Saka, Cole Palmer, Jack Grealish and Phil Foden have all pulling out.
Kane has said that "England comes before anything", with the Bayern Munich striker suggesting that some players have "taken advantage" of the situation to ensure that they are available for their clubs at a key stage of the season.
"[Gareth] Southgate brought the joy to play for England back," Kane told ITV Sport. "Every camp people were excited to come, every camp people wanted to play for England and that's the most important thing.
"I think England comes before anything. England comes before club, it is the most important thing as a professional footballer. Gareth was hot on that and he wasn't afraid to make decisions if that started to drift from certain players.
"It's a shame this week, obviously. It's a tough period of the season and maybe that's been taken advantage of a little bit. I don't really like it if I'm totally honest. England comes before anything and any club situation."
Kane insists that "England comes before anything"
England are currently second in Group 2 of League B, picking up nine points from their four matches, which has left them three points behind section leaders Greece ahead of Thursday's battle.
The Three Lions will then round off their group-stage campaign against Republic of Ireland on Sunday evening.
Lee Carsley is coming to the end of his time as interim manager, with Thomas Tuchel, who left Bayern Munich at the end of last season, set to take over the national side at the start of 2025.
Tuchel has penned an initial 18-month contract to take him to the end of the 2026 World Cup, and the German will be expected to oversee a strong challenge for the trophy in the tournament.
Rogers has benefitted from England withdrawals
Aston Villa's Morgan Rogers has benefitted from the withdrawals, with the attacker earning a promotion from the Under-21s, and he is determined to make his mark during the camp.
"Obviously, I'm a big England fan, so I watched all the internationals growing up. So playing with these players now is a pinch-me moment," the 22-year-old said.
"But I'm just really excited to learn what it's all about and to show what I'm about at the same time. I'm enjoying my football at the moment. I think I'm playing pretty well, but I know there's obviously still work to do and work to improve on.
"I'm so thankful and grateful I'm here, now I can say that I've finally been called up and it's a great honour. "I think I just try and push myself every day and see what new levels I can reach.
"I've probably surprised myself at times, maybe this season, with how well I've done, but I've always had that confidence and that belief in myself that I can get to this level and maintain it. It's more about maintaining my consistency, keep it going, and hopefully I can get better and better and just keep improving."
Rodgers has been a key player for Villa during the 2024-25 campaign, making 15 appearances in all competitions, contributing three goals and three assists in the process.