The American Post entire did much of the work before getting tired and eventually finishing third as Hunaina sprang a surprise in the Prix Montjeu for trainer Henri-Francois Devin in the hands of Alexis Badel.
"We were pleased. It was a funny sort of race and he was only beaten a length and a half," said Dunlop.
"Cristian Demuro reported in that the horse didn't quite like the Polytrack and would be better on turf but, more importantly, he just got a little bit tired in the final furlong.
"The filly that won it was getting 12lb from us and we were also just half a length away from a Group One performer (Trais Fluors). For a first start of the year, we were pleased. Obviously we would have liked to have won.
"It's onwards and upwards, with something like the Earl of Sefton next at Newmarket."
Hunaina was bought at Goffs November Sales for €140,000 out of Michael Halford's Irish stable and was having her second start for Devin.
Robin Of Navan was soon in front, but Hunaina was always hot on his heels and he had no more to give when headed.
Trais Fluors looked a big danger but Hunaina (13-2) stuck to her guns to score by three-quarters of a length from the 4-5 favourite Trais Fluors. Robin Of Navan was the same distance away in third.
Talismanic warmed up for the Dubai World Cup when landing a cosy victory in the Prix Darshaan.
The Breeders' Cup Turf hero was last seen finishing second to Highland Reel in the Hong Kong Vase at Sha Tin in December and returned to winning ways with a likeable performance over his Andre Fabre-trained stablemate and fellow Godolphin-owned runner Cloth Of Stars.
Maxime Guyon had Talismanic perfectly positioned as Savoken made the running before asking him to take over in the straight.
Talismanic (13-10) soon went on and comfortably held Cloth Of Stars, the 4-5 favourite, by a length and three-quarters, with Savoken three and a half lengths away in third.
"We were very pleased with Talismanic, Cloth Of Stars and Rosa Imperial, who all appear to be in good form physically and mentally, " Godolphin's Lisa-Jane Graffard told their official website.
"They will all come on for their races today and will fly out to Dubai at the end of this week to continue their preparation for Dubai World Cup Night."
Trained by Fabre, Rosa Imperial was beaten three-quarters of a length when second to City Light in the Prix Anabaa, a Fast-Track Qualifier for All-Weather Championship Finals Day at Lingfield on Good Friday.
Winning trainer Stephane Wattel said: "It was a quality field today and City Light did it really well.
"We already saw he ran well on his first time on the all-weather, and today he showed that the distance and surface was perfect for him.
"This was my first runner this year of those that haven't been running all winter.
"I have to speak to the owners (Ecurie Jean-Louis Bouchard), but I'd really like to go to Lingfield with him. I think the track should suit him at Lingfield.
"It's a very good championship and I ran him in this race specifically to qualify."
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