Sturridge capped off the scoring with his first touch after coming off the bench, continuing his good pre-season form with a close-range finish two minutes from time.
The 28-year-old had been linked with an Anfield exit this summer, but Klopp believes that the striker will provide his side with a useful option if he is able to stay fit.
"What was it, 10 seconds? 12 seconds?! Sometimes you need luck in life. He didn't need luck in that situation; he only has the nose for it in those situations. It's brilliant," Klopp told Sky Sports News.
"Sturridge had a fantastic pre-season, the best since I've been here, and it gives us unbelievable new options."