James Milner‘s fifth-minute penalty, awarded after Dominik Kohr handled, proved decisive in the 1-0 victory which put the Reds into the last 16.
However, just as significant was seeing Sturridge – starting a third successive match for the first time since last March – and Coutinho, who took a couple of hefty knocks, get through the game with the Capital One Cup final against Manchester City to come on Sunday.
“After the game with a 1-0 I am completely fine as I know there are no injuries,” said Klopp, who will discover Liverpool’s opponents in the next round when the draw is made at midday on Friday.
“It is important, this is what every player will tell you, that you need to know you can carry on in a situation when it is harder.
“Phil had one or two situations after challenges but we need to find new faith or trust in the body of the players.
“They (Sturridge and Coutinho) are very important for us but we need them in best shape and you can only get this from training and matches.”
Liverpool missed a number of chances with Sturridge as guilty as any but the England international benefited from starting another match alongside Coutinho and Roberto Firmino.
Klopp knows the striker will be key for him in the Wembley showpiece and so played down the effect of the result and the performance as a whole.
“It is better than if we had had a defeat or been knocked out,” he added.
Liverpool 1-0 Ausgburg
“It is not relevant to Sunday but the team has benefited from a good performance – but you could say same about City in Kiev last night (where they won 3-1 in the Champions League).
“We will try our damnedest to get a good performance on Sunday.”
Those missed chances meant Liverpool had to survive a nervy final 15 minutes but Klopp was in no doubt his side fully warranted victory.
“If you can’t decide the game early enough that is how it is,” he said.
“After 70 minutes we were that good that we couldn’t see their plan and the free-kick was the biggest challenge up front for us.
“It was absolutely deserved. We were the better team, we created chances but we had one problem in that we didn’t use them.
“We couldn’t control the game in the last 20 minutes and it was hard, that is how it should be, but we are in the next round.”