The world No 8 and top seed made a superb start in Nottingham but was pegged back and then edged out in a tight finish to lose 2-6 7-6 (7-3) 7-5 to the Croatian.
Konta looked to have overcome a mid-match wobble as she recovered to lead 5-4 in the final set but Vekic struck back to claim her second singles title.
“All credit to Donna, she was continuously able to raise her level all throughout that match,” Konta said. “I was not able to stay with her.
“But I’m very happy that I got to play five great matches on the grass. For Donna and I, heading into Wimbledon, we just want to play on the surface as much as possible.”
Konta broke Vekic in the first game of the match and powered through the opening set in commanding fashion.
Vekic’s recovery started as she broke to lead 3-1 in the second set. Konta immediately broke back but there were signs of frustration as she disputed a line call.
She lost the set on a tie-break and there was further anguish early in the final set as she contested another decision.
Again she fell 3-1 behind but after recovering to draw back level and then lead, it seemed she held the edge. But after serving to stay in the match, Vekic claimed a crucial break and then served out for victory.
Vekic said: “It’s pretty amazing. It’s my first grass-court title and my second overall. I’m really happy.
“Jo played amazing, she’s having an amazing year, but I was just trying to focus on myself and serve as good as I can and be aggressive.”
Meanwhile, on the ATP Tour, France’s Lucas Pouille came from behind to claim his second title of the year with victory over Feliciano Lopez in the Mercedes Cup final in Stuttgart.
The world No 16 hit 29 aces on his way to a 4-6, 7-6, 6-4 victory, which also marked his third tournament success since last September. The match was tight throughout but wildcard Pouille closed out in style with an ace.
The 23-year-old said: “I think I took a little bit more of the opportunities than him. He had some break points and didn’t make them, and I had only one or two and I made them. So I think that made the difference.”
Lopez took the only break in the first set but Pouille saved four more break points in the second and went on to edge the tie-break 7-5.
Pouille then took advantage of a break point at 2-2 in the third set and managed to hold on to his lead.
Fourth seed Gilles Muller won the Ricoh Open in s-Hertogenbosch with a hard-fought 7-6, 7-6 win over fellow veteran Ivo Karlovic.
Neither player was able to force a break of serve in the match but 34-year-old Muller had the edge over his 38-year-old opponent in both tie-breaks.