The manager said the striker’s horror miss changed the game.
Sturridge, who was handed a rare start by Klopp, missed an empty net from just six yards out after 17 minutes.
The England striker was replaced by Roberto Firmino at half-time and Klopp thinks his miss might have swung the momentum in the hosts’ favour.
“The start was intense, that was clear,” Klopp told reporters after the match.
“Red Star wanted to strike back, which they did.
“We had the first big chance with Daniel, a very big one.
“Each goal in a game like this leads the game in a specific direction.”