Sturridge started the Premier League game between Swansea City and Liverpool at the Liberty Stadium on Sunday afternoon and played for the entire 90 minutes.
“I spoke to him at half-time,” Klopp told Liverpool’s official website when asked about Sturridge playing for the entire 90 minutes against Swansea.
“We’d already made two changes, so if he felt something he should give me a sign but he said ‘no, I want to play the 90 minutes’.
“It’s absolutely no problem. He didn’t play on Thursday, so now we have four or five days until Thursday again, so everything is good.”
Sturridge failed to score at the Liberty Stadium, as 10-man Liverpool went down 3-1 to Swansea.
The England international striker took four shots, had a pass accuracy of 79%, put in one cross, attempted three dribbles, and made one interception and one clearance.
The former Chelsea and Manchester City man has scored eight goals and created five chances in 13 Premier League appearances for Liverpool this season.
Sturridge has a pass accuracy of 79% and a shot accuracy of 57%, and has won five headers, 10 dribbles and one tackle.
Liverpool will take on Spanish club Villarreal at Anfield in the second leg of the Europa League semi-final tie on Thursday evening.
Sturridge has taken to Twitter to share his hopes for a win against Villarreal, and has also thanked the Liverpool fans for their support against Swansea on Sunday.
Absolutely gutted. Thanks to the fans for travelling and supporting us. God willing Thursday will be a better result.— Daniel Sturridge (@DanielSturridge) 1 May 2016