The home side bounced back from a 12-9 loss to Bath to score five tries and keep their unbeaten run against Sale going, moving up to fifth in the Aviva Premiership in the process.
Baxter said: "I think the players wanted to put the record straight after the relatively close loss to Bath, but they also wanted to put the record straight after what happened at Sale when many felt that the Sharks had thrown it away.
"Not many talked about how well Exeter played for the last 60 minutes up there to come away with a win. So we felt that we had a point to prove and we wanted to show that we could score tries.
"We are a good rugby side, we have got ambition, we are looking up the table and hunting things down rather than worrying about other stuff. We showed that in this game.
"We are aware that we have had some tight games recently but the reality is that in the last three games we have scored one try but only conceded one try; they weren't high-scoring, big-tempo games.
"Fourteen points from four games is pretty good going, it is above our target slightly, we felt that we had the opportunity to get around 12 points. We are moving in to the business end of the season now with one our best, energetic performances."
Sale have not won away from home in the Premiership since they beat Bath in September and head coach Tony Hanks was "gutted' by the defeat.
Hanks said: "There are no arguments or excuses from us on the result because they [Exeter] truly deserved what they got and they were better than us in all aspects of the game and deserved their win.
"We didn't start well but the wind was significant and if we had gone in [to the break] 11-0 down there was an opportunity to regroup and try and sort some bits of our game and get some ball in play because it was quite stop-start.
"But at 18-0 that was going to make it tough against a pretty good side. Then we were guilty in the opening stages of the second half of trying to put everything right but we let them score again and it was effectively over as a contest.
"We had a couple of nice moments but they were very much a consolation. We felt that we had been playing very nicely over the past three weeks, we've played some good rugby and probably trained the best in the past week.
"The motivation was high, considering what happened at our place and we got beaten. So we need to go away and regroup but the worse thing for us is that we don't play for three weeks and that makes it really hard."
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