Raducanu, ranked 42nd in the world, seemed hampered by a leg issue as Vekic cruised to the first set in less than half an hour.
The British number one rallied superbly to move a double break ahead in the second set, but twice failed to serve out victory – and could not convert two set points at 5-4.
Vekic, who is ranked 76th but adept on the grass, is an experienced campaigner and held her nerve to level.
Both players looked to be tiring in a physical encounter, but Raducanu – backed by a vociferous home crowd – dug deep to force a tie-break.
Despite the defeat, Raducanu will take a lot of pride from an encouraging week on the British grass as she builds up towards Wimbledon.
Raducanu’s season has been disrupted by a viral illness, meaning she was limited to only playing six matches from early February up to Queen’s.
The ranking points she has earned in west London will push her up to the brink of the world’s top 30, which could be enough to ensure she is seeded at the All England Club.
“I haven’t really played much this season, but to think I have made two finals so far, which I haven’t done in years, it has to be, in a way, celebrated,” said Raducanu, who lost in the Cluj final in February.
“It’s a good achievement for me and I’m proud of it.”
