Klopp's fortunes took a turn for the better when Liverpool beat Stoke 1-0 in the first leg of their Capital One Cup semi-final on Tuesday night.
But his training methods have been under fierce scrutiny since Philippe Coutinho, Dejan Lovren and Kolo Toure all picked up injuries at the Britannia Stadium, with Sunderland manager Sam Allardyce claiming that a spate of hamstring problems were down to the German's insistence on a high-tempo pressing game.
Coutinho, Lovren and Toure all miss the trip to Devon on Friday night to take the number of Liverpool absentees to 11, forcing Klopp into making further changes against the Sky Bet League Two minnows.
"We have to make decisions in this moment for the team, so we have to make changes," Klopp said ahead of the third-round tie.
"That is all I can say because I don't know who is available.
"The team which will play will want to win this game for sure, but it will be a team that hasn't played too often together."
With Barclays Premier League leaders Arsenal set to visit Anfield on Wednesday, Klopp will be tempted to leave one or two frontline players out at Exeter despite the lengthy nature of Liverpool's injury list.
But Klopp insists the seven-time FA Cup winners will treat the competition with the respect it deserves.
"It is a big tournament and we have a big respect for it," Klopp said.
"We have to find a solution. If we go out you have to criticise us, no problem, but we have to think about more than only one game.
"Everyone wants to see the sensation (of an upset) and if this is a chance for Exeter then they have to take it.
"I saw after the rain the pitch is not in the best shape.
"The dressing room should be small, I heard, so maybe we should not spend the longest time in it and go out and play football!"
Out-of-form Exeter have slipped to 16th in League Two after losing four successive games, three of them at their compact St James Park home.
But Grecians boss Paul Tisdale promises Liverpool will be meeting fearless opponents in front of the live television cameras.
"We are not just going to sit back and defend," Tisdale said.
"I don't want to do that, we need to have some intent about us.
"I don't think we should hold back and wait for the game to happen.
"It's a compromise between how much you risk, but we can play with no fear."