The Premier League leaders surrendered a two-goal advantage against the League One side on Sunday after Klopp had made nine changes to the starting line-up.
At least four Premier League teams will need replays, which are scheduled for Tuesday 4 and Wednesday 5 February, meaning they will cut into the new mid-season break which runs between 2 and 16 February.
“I said to the boys already two weeks ago that we will have a winter break, which means we will not be there,” said Klopp.
“You cannot deal with us like nobody cares about it. I know that it’s not very popular but that’s the way I see it.
“The Premier League asked us to respect the winter break. That’s what we do. If the FA doesn’t respect that, then we cannot change it. We will not be there.”
Klopp said it “will be the kids who play” and also confirmed that reserve coach Neil Critchley, who took charge of the Carabao Cup quarter-final loss to Aston Villa in December while the first team were playing the World Club Cup, will again be in the dugout.
“We have to respect the players’ welfare. They need a rest. They need a mental rest, a physical rest, and that’s what the winter break is all about,” said Klopp.
“We had to make these decisions beforehand because these boys have families.”
As well as Shrewsbury’s visit to Anfield, Newcastle will travel to Oxford after a 0-0 draw at St James’ Park.
Tottenham and Southampton will have to meet again after drawing 1-1 on the south coast, with the date currently set for Wednesday, 5 February.
All replays could be moved for TV coverage.
What and when is the winter break?
This is the first season the Premier League has scheduled a winter break, albeit with a different format to leagues on the continent who take a few weeks off over Christmas.
In a letter sent to clubs from the Premier League in March, teams were told they were “expected to honour and respect the underlining rationale for the mid-season player break, namely to provide their players with a break from the physical and mental rigours of playing matches during the season”.
“Clubs should not arrange competitive or friendly matches with other clubs during the mid-season player break,” the letter continued.
In the winter break, four Premier League matches will take place on the weekend of 8 February, with the other six the following weekend – with all the games on at different times and televised.
This means that every team should have 13-16 days between games.
But it may not pan out like that…
Southampton are the worst affected and will only have 10 days between their replay against Spurs, if it is played on 5 February, and a home game against Burnley in the league.
“Because the rules are not the best, we have another game, in a break in the season,” said Saints manager Ralph Hasenhuttl, who has managed in the German Bundesliga. “I don’t understand this but, OK, we have to do it. It’s for us not perfect but we must accept it.”
Spurs and Liverpool will have 11 days off instead of two weeks.
If Newcastle have to play their replay at Oxford on 4 February, three days after a Premier League game against Norwich, they will only have 12 days off before their trip to Arsenal.
Had any of those sides been scheduled to play in the first weekend of the winter break, they would have had two full weeks off.
“It’s a ridiculous situation,” said Bruce. “You’re supposed to have a week off then all of a sudden they’ve shoved replays in there. What’s the point?”
When else could the replays be?
It is understood the FA is committed to working with clubs to maintain a winter break for Premier League teams. But it is unclear where any rearranged games could be moved to.
The fifth-round games are on the week starting Monday, 2 March – scheduled for midweek for the first time to help free up Premier League teams for the winter break – so replays would clearly need to be played before then.
Oxford play nine games in February – on every Saturday and Tuesday (subject to the final date of the Newcastle game) so there are no free dates for their replay.
The midweek after the replays are scheduled would fall in between the two rounds of winter-break Premier League games so make even less sense, and the week after that (starting 17 February) sees Spurs and Liverpool play in the Champions League.
Spurs and Southampton are free on the Tuesday and Wednesday before the fifth-round ties, although the game would have to be played on the same night as Champions League ties.