Trailing 2-0 after 20 minutes, England hit back with two goals both before and after half-time to take the lead with Kate Walsh's late double completing the turnaround.
Walsh netted in the 63rd and 70th minutes while Lily Owsley bagged a double herself and Alex Danson and Georgie Twigg one each as England got their campaign up and running.
England face the Netherlands next, the Olympic champions defeating European gold medallists Germany 6-0 in their first game, with Lee concentrating on the positives against Korea.
"It wasn't a great start of course going 2-0 down but we managed to change a few things around and in the end I thought we quite comfortably won and could have scored even more," he said.
"I'm also glad we scored quite a few goals because it's such a tight pool of top-class teams and I think goal difference could play a big part in deciding positions.
"We're not used to playing Korea, especially having just had the summer with the Europeans; we've got quite used to playing a certain style.
"I thought it was a really good test for us and the girls showed great resilience to come through with a 6-2 victory in the end."