The third tier club came from 2-0 down to earn a draw and date at Anfield with the Premier League side but a frustrated Klopp announced Under-23's manager Neil Critchley would stand-in.
The Reds fielded their youngest ever team with the starting line-up having an average of 19. But Critchley's side were victorious with a 1-0 victory. Klopp made the decision because the replay was due to take place in the Premier League's 'winter break' and several of his stars jetted off for a week of rest.
Shrewsbury outlined their anger in a club statement following the curtailment of the League One season on Tuesday.
"You will recall our incredible come back in the FA Cup Fourth Round tie live on BBC with Liverpool to draw 2-2 back in January.
"Immediately following the match, the Liverpool manager Jurgen Klopp ruined what should have been a wonderful moment for our club by making public statements that he and all of his first-team would not attend the replay at Anfield, effectively ruining what should have been not just financially but for the players and fans a wonderful achievement and a very special occasion.
"We struggled to believe that his statements had no effect on the replay being televised and we are convinced that LFC broke the FA Cup rules by not "fielding their strongest team" in the return fixture which had a knock-on effect of STFC not getting anywhere near the financial rewards that were to be expected from an FA Cup Fourth Round replay including a potential live TV fee against the World & European Champions and Premier League Champions (elect).
"In February we put a complaint in to the FA about the alleged rule breach but unfortunately and quite unexpectedly we were informed that this was dismissed last week (four months on).
"This without doubt resulted in a much lesser occasion for our players and fans as well as the financial reward that would have been expected from LFC playing their strongest team and abiding by the FA Cup rules."