The British number two again qualified for an ATP tournament and had been hoping to build on his run to the semi-finals in Zagreb, but he lost out 3-6 7-6 (7/4) 6-4.
He began very well against Ukrainian Stakhovksy, who stunned Roger Federer at Wimbledon last year, and took the first set.
Evans saved all 13 break points he faced in the first two sets but Stakhovsky levelled matters on a tie-break and then finally took his chance at the start of the decider.
Evans, ranked 124, fought back from 5-2 to 5-4 but could not complete the comeback.
It has nevertheless been another decent tournament for the 23-year-old, providing more valuable ranking points in his quest to reach the top 100.