After a difficult start to the season under Brendan Rodgers, Sakho has established himself as a key member of Klopp's starting XI in the early days of the German's reign on Merseyside.
The France defender has always enjoyed a strong relationship with the Liverpool faithful following his move from Paris Saint-Germain in September 2013, and his name was sung loudly throughout Thursday's 1-1 Europa League draw with Rubin Kazan at Anfield.
Sakho responded with a superb display - and a salute to the Kop at full time - and his new manager has been impressed by the 25-year-old.
When asked why Sakho was out of favor under Rodgers, Klopp replied: "I can't say anything about this. Maybe he was not fit or things like this. But I can understand why they shouted his name. Mama was really spectacular defending and good playing football [against Rubin]."
Daniel Sturridge missed Thursday's match with a minor knee problem sustained in the lead up to Klopp's first game in charge - last weekend's 0-0 draw at Tottenham - and he remains a doubt for Sunday's clash with Southampton.
Sturridge has endured an injury nightmare over the last 12 months, and Klopp says any top team would struggle without its frontline forward for a sustained period.
"There are two things in football make a difference, the way you play and the players," the former Borussia Dortmund coach added. "Sometimes you need this striker, of course you always need a finisher, someone for the last ball. [Christian] Benteke and [Roberto] Firmino were in three days of light training and because of our situation they were in the squad on Thursday.
"If you take [Lionel] Messi out of Barcelona for about a year, ask them how they feel? If you take [Sergio] Aguero for one year out of Man City, ask them how they feel? If you take [Robert] Lewandowski... things like this, that's always the same in football."