Liverpool remain in the Carabao Cup.
Pedro Chirivella replaced Naby Keita just after the hour mark at Stadium MK, but the Spaniard's necessary paperwork to play a part in the competition was not processed and international clearance hadn't been received.
It means the Reds' place in the next round is safe and Klopp's men will meet Arsenal at Anfield on October 29.
A Liverpool spokesperson said: "The club accepts the judgement, outcome and punishment imposed by the EFL.
"We believe it is proportionate with the technical indiscretion committed and will be making no further representations.
"Even though there were mitigating factors, which were beyond our control or jurisdiction, we believe it appropriate we apologise to the competition's governing body and also to Milton Keynes Dons."
An EFL statement read: "The club's breach was in part due to the challenges it encountered with securing the correct international clearance, and its subsequent ability to include the player on team sheets despite the lack of clearance.
"As a result the board concluded the most appropriate sanction was a financial penalty."