Priestland slipped early in the second half at Parc y Scarlets and was taken from the field on a stretcher before sitting in the stand later wearing a protective boot.
He is expected to go for a scan on the injury.
"He has got an Achilles injury," confirmed Scarlets head coach Simon Easterby.
"We won't know the extent of that until he has a scan. But it didn't look good."
The Scarlets also lost flanker Aaron Shingler with a hip injury 16 minutes from time.
"Aaron Shingler suffered a groin injury and he's been carrying that for a couple of weeks. Hopefully he will come through but that didn't look great either," added Easterby.
Those two injuries compounded a bad day all round for the Welsh side, with Gareth Steenson kicking 17 points in Exeter's first-ever Heineken Cup win.
Haydn Thomas gave the visitors the perfect start with a try on five minutes and the Chiefs led throughout from there on.
It meant Scarlets, who did grab back a late penalty try from a scrum, crashed to a third straight European defeat.
Easterby added: "You can't give any side the start they had and we slipped off a couple of tackles and they scored a soft try and they scored a couple of points from our error and indiscipline.
"The second half was much better. We played a lot more tempo and we won the second half 10-6.
"When you give a side the start we did it was always going to be difficult to get back into the game."
Exeter coach Rob Baxter was delighted for his team to get their first ever Heineken Cup success after defeats to Leinster and Clermont Auvergne.
"It's our first Heineken Cup win. Nice to collect some points and do it on the road against the Scarlets who have a fantastic Heineken Cup tradition," Baxter said.
"We came into the season saying we wanted to compete in the Heineken Cup and we did that pretty well in the first couple of games.
"The next thing on the line was to force a win. It wasn't the greatest game of rugby but I think we did enough to win the arm wrestle.
"We wanted to come into the competition giving a good account of ourselves. Ultimately this [the Heineken Cup] is a big learning curve as a club."
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