The English forward made his long-awaited return to action on Sunday against Swansea City following a string of injuries, much to the delight of Reds fans.
It was originally thought Sturridge would be available for the Anfield side's Europa League clash against Bordeaux last Thursday, which they won 2-1, only for the 26-year-old to pull out at the last minute.
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He was sent for a scan to establish the extent of the niggle, but nothing major was revealed.
The striker now appears to be on the road to recovery following his cameo against the Swans, but Klopp believes he must push through the pain barrier rather than succumb to each and every supposed injury.
Speaking prior to their 1-0 win, he said: "Your body has to learn new intensity of training and you have to learn what is serious pain or what is only pain. Of course everyone wants him back on the pitch."
"We have to accept the situation, he’s often been injured in the last few months, maybe year.
"I understand why everyone is waiting. If it wasn’t someone with the quality of Daniel no one would think about it.
The frustration amongst fans and Klopp himself is understandable, of course. Sturridge has made just seven league starts since October 2014 and it seems whenever the England international is close to a return, another injury presents itself.
A brace against Aston Villa late September spelled what seemed to be his return to action following a year of struggle, but a knee injury in training mere weeks later ruled him out once again.
"It has been a really long period out now we have to stay patient I am sorry to say," Klopp continued - and he's bang on the money.
Far too often players are rushed back from injury and in Sturridge's case, patience is a necessity to ensure he's at 100% fitness before a full comeback into the starting line-up.
However, coinciding with patience must come Sturridge's willingness to play through pain, both for his own development physically and mentally, and for his team-mates' sake.
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