Liverpool needed the lottery of the penalty shootout to beat the Gunners in the Carabao Cup fourth-round after a pulsating game at Anfield ended 5-5 in regulation time.
The Carabao Cup quarter-final matches are set to be played on December 16, and the Reds will be participating in the Club World Cup, with their semi-final match scheduled for December 18.
Klopp was adamant that his team would only be available to play in the next round of the Carabao Cup, if the EFL could find a suitable date in the middle of their busy fixture list.
“We will not be the victim of this problem,” Klopp told reporters after Liverpool’s game.
“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.”