The England international made the breakthrough in the first half from the penalty spot after Nathaniel Clyne was fouled by Memphis Depay.
The Merseyside outfit doubled their lead in the first leg of their Europa League last-16 clash after Roberto Firmino finished from close range.
Sturridge was replaced by Joe Allen in the second half at Anfield which prompted some concern that the injury-prone striker may have aggravated a problem.
But Liverpool manager Klopp revealed that there was no issue and heaped praise on his replacement, Allen.
“It was a little bit of everything [protecting Sturridge and easing him back to fitness],” Klopp told BT Sport.
“It was the moment when we didn’t have control in midfield so we changed system.
“Joe Allen came on and I’m really pleased for him.
“He had a long injury and he came back in really good shape but he is not playing. It is really hard. I don’t like this.
“He showed how strong he is.”
Liverpool aren’t in action again until their second leg at Old Trafford next Thursday.
The Reds’s 2-0 victory ended a four-game losing run against their bitter rivals in all competitions.
The Merseyside outfit are in sixth place and three points behind United in the Premier League.
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