Klopp's Liverpool overcame a wild clash with Arsenal at Anfield, where the European champions prevailed 5-4 on penalties after a remarkable 5-5 draw on Thursday (AEDT).
Liverpool twice came from behind against Arsenal in a stunning comeback on Merseyside, but Klopp quickly threw his team's quarter-final participation in doubt afterwards.
Champions League holder Liverpool is due to feature at the Club World Cup, which will be held between December 17-21 in Qatar – the same week the Carabao Cup quarters are scheduled to take place.
"We will not be the victim of this problem," Klopp told reporters post-game midweek. "We play tonight, we wanted to win it, we did that, and if they don't find a proper date for us, then we cannot play the next round and whoever is our opponent will go through. Or Arsenal play them.
"I'm not concerned, somebody else has to be concerned because we didn't make the fixture list, we didn't make the schedule.
"I've said it already, FIFA told us the Club World Cup will be there [Qatar] and we have to come there and we will do. The Premier League tells us we have to play in the Premier League, which we do obviously.
"The Carabao Cup, what we did tonight, if they don't find an appropriate place for us, not 3am on Christmas Day, then we don't play it. They have to make that decision. You have to think about these things.
"If you have a fixture list where one team cannot be part of all the games, then you have to think about the fixture list. Hopefully it starts now. I really think that's fair, and this problem is obvious now.
"We are going to ignore that problem completely for tonight. A lot of people from the Premier League were sitting in front of the television hoping that Arsenal can do it. But, I'm sorry."