On a day of celebration as captain Steph Houghton received her 100th cap, the Lionesses found themselves behind as early as the 19th minute when Sofia Jakobsson punished slack England defending.
The visitors also hit the post before doubling their advantage in the 33rd minute as the Lionesses once again failed to clear their lines, allowing Anna Anvegard to rifle home from close range.
Although a friendly encounter, it leaves boss Neville with plenty to think about ahead of next summer's Women's World Cup to be held in France.
Before the encounter there would have been plenty of optimism surrounding the Lionesses' chances of going one better than the semi-final showing in Canada back in 2015.
But worryingly the Lionesses found themselves second best for the majority of this encounter; Jakobsson taking full advantage of too much time on the edge of the box to bend a strike into the corner of Carly Telford's net.
England continued to offer very little in the final third in the opening 45 minutes while Sweden looked ominous in attack - Caroline Seger heading against the woodwork from a deep, right-wing corner just past the half-hour mark.