Ospreys took the lead through Dafydd Howells who burrowed over from close range only for Exeter hooker Lloyd Cowan-Dickie levelling things up at the other end from a similar range.
Tom Grabham pounced on a bouncing ball to set up Morgan Allen who crossed to give the Ospreys a 10-8 lead at the break, before Exeter struck back with a quick-fire pair of scores from James Scaysbrook and Cowan-Dickie again.
But Ospreys refused to give in, with Matthew Jenkins and Grabham scoring well-worked tries after quick passing in midfield.
Exeter finished the stronger however, James Phillips and Don Armand crossing to seal a 36-22 victory for the home side, although Rees refused to be too downhearted in defeat.
"We are disappointed," admitted Rees. "We came here to win a game of rugby, and to be on the wrong end of the score-line is frustrating.
"We were outgunned at times, and lost some aspects of the power battle, but we have a young group of players who we want to be positive with.
"We are trying to develop a brand of rugby and put some width on it and challenge defenders, and we have got to be pleased with that and the tries we scored, whilst also leaving another three or four out there.
"That in itself is pleasing because, in LV= Cup games over the past couple of years, we have dug in, been tough and had a go, but ultimately perhaps not shown where we want the team to go, so at least this is something we can hang our hats on and be relatively pleased about."
Follow us on Facebook, join the conversation on Twitter, sign up to our YouTube channel for extensive match highlights and sign up to our newsletter for regular updates on the RaboDirect PRO12
Guinness PRO12 Ospreys News
63x46.png){kind=logo}