The striker made a quick exit after the loss to Swansea City, to much criticism.
It was a frustrating afternoon for Klopp’s side, and particularly Sturridge who was on the periphery for much of the clash.
After the game he headed straight down the tunnel while some of his teammates clapped the fans in the centre circle, receiving some criticism for doing so.
Klopp though, says that it is his fault rather than the striker’s and any criticism should be aimed at him.
"If somebody forgot to say something to the fans then it's my fault," he told the Independent.
“It is nobody else's fault. If you think we ignore the fans it's not what we wanted. I went too immediately.”
“Hopefully our fans know how close we are to them. After a game like this if you want to leave, if you want to go... you (might) want to rest and recover and do a lot of things."
While Klopp was determined to turn attention to himself rather than his player, there is no denying Sturridge is a frustrated figure at present.
The decision to leave him sat on the bench for the Europa League semi final against Villarreal recently will not have gone down well and has sparked talk of an exit in the summer.
Many feel he should be a regular starter, but Klopp clearly doesn’t, and it will be interesting to see how this incident affects his future at Anfield.