The Chiefs scored four tries as they convincingly won their first ever match against the Welsh regional side.
"It was a good win with a very important bonus point," said Baxter.
"One thing that we learnt from these competitions last year was that not getting a bonus point when you need one often makes the final stages pretty tough.
"We did pretty well in the pool stages of the LV= Cup last year but didn't qualify, so for us now to get that bonus point at home is important, It means that it gives us something really to fight for next week at Saracens.
"Plus when the LV= Cup comes round again in the new year it stays an important competition for us and I think that is what you have to do. You have to stay in the competition and make as many games important as you can.
"In this competition some sides are going for it more than others, some teams have slightly stronger squads than others, and some teams were throwing a fair bit of youth development into it.
"That is what the competition is and you don't know really what you are going to come up against. We faced quite a young and enthusiastic Ospreys side and they took a bit a bit of taming.
"For us, I was very pleased that our disjointed side came together and had to fight for 20 minutes, when they looked a pretty accomplished side."
Exeter went into the break 17-6 in front after a penalty try and a touchdown from lock James Phillips, with skipper Gareth Steenson converting both and adding a penalty.
Ospreys' points in the first period came through two penalties from 19-year old fly-half Matthew Morgan in his first start of the season.
Steenson and Morgan exchanged penalties early in the second half with the Chiefs adding tries through outside centre Phil Dollman and replacement inside centre Josh Tatupu with Steenson converting the second.
Ospreys had given Bridgend head coach Steve Tandy the reins for this game and next weekend's cup tie against Northampton.
Tandy said: "We were obviously disappointed with the score and I feel a little disappointed with the set-piece plus our disjointed second half but there were a lot of positives to take from the game.
"We had brought a young group of players - probably six or seven of them making their debuts for Ospreys which is a positive from us, giving them experience of where they need to be to be an Ospreys player."
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