Klopp's side were held to a 0-0 draw by United at Anfield on Monday in a largely forgettable stalemate.
Sturridge was handed a starting spot but failed to impress before being removed from the action and replaced by Adam Lallana on the hour mark.
Klopp has stressed he isn't too concerned by Sturridge's underwhelming display on Monday, indicating the England international didn't get the service he required to make a real impact.
He told the Liverpool Echo: "It was a really difficult game for a striker, the way we played it wasn't easy to enjoy for a striker.
"In the first half Phil [Coutinho] made a brilliant run and wanted to pass to Daniel but [Sadio] Mane was free on the right.
"We had a really good attitude, the players worked really hard and tried everything, but only with the wrong tools."