But there was no such cause for celebration for Sale's new director of rugby Bryan Redpath on a day which saw Danny Cipriani make his debut for the club.
"As a coach getting that first result brings a bit of relief as we all start on no points," admitted Baxter.
"We had a nice finish to last season where we were comfortable and we could get after games.
"We have kind of taken off in the same manner, which is really pleasing, but the scoreline probably doesn't show that the game was massively competitive for very long periods.
"We were just shading enough of them to give us momentum and once you get a couple of scores up and team have to start coming back at you, the game shape changes.
"As it opened up we managed to exploit some opportunities but great credit to our players who had to work extremely hard for a long time to make these cracks appear.
"We have said to the guys to be as competitive as we can, in every area of the pitch, and the little bits will add up.
"We were good in a lot of little areas - our lineout was competitive on their ball, our scrum was competitive on both put-ins; our breakdown work was good - there was lots of little things that put pressure on Sale and kept the pressure off us."
Exeter went in to the break 14-3 ahead after their Argentinian international fly-half Ignacio Mieres scored all their points through a try and three penalties and his Sharks counterpart Nick MacLeod replying with a penalty.
Baxter added: "Coming in at half-time we were far from comfortable - we knocked over a penalty just before break which opened up a little bit of breathing space.
"But the game was still there for someone to take hold of and what we did after half time was to take hold of it. The single most pleasing things was the guys being so competitive in so many areas of the game."
The Chiefs stretched their lead in the third quarter with tries from lock Aly Muldowney and Matt Jess. Mieres added a penalty while MacLeod again answered with a penalty.
Exeter's bonus point try came on the hour through flanker Tom Johnson followed by replacement prop Chris Budgen claiming the sixth try of the game, which replacement Gareth Steenson converted.
The defeat means that the Sharks have lost all five encounters with the Chiefs and Redpath said that he was honest with the players in the dressing room after the match,
He added: "Any team that does that isn't going to win or come close. To play any team in the Premiership that [the performance] wouldn't have been good enough so there is no hiding place for it.
"It wasn't the game plan not been heeded but individual errors and our detail was poor so we never got to our game plan because there were 10 set pieces that we gave away and they scored on three them.
"There were too many individual errors across the board from lots of people and we all have to take it on board and take the criticism that comes. Quite rightly it deserves to come.
"We have Saracens next Saturday and we can't forget this game nor can we dwell on it. We have to man up and take the criticism and show a good performance next weekend which has to be a lot better than this."
Former England fly-half Cipriani made his Premiership debut for the Sharks when he came off the bench after 30 minutes when his side were trailing 11-3.
Redpath added: "He never had a chance to show his ability. Danny's game is hopefully about getting possession on the front foot and we never got any of that.
"Danny is a talented player but there was nothing in this game to hang a hat on."
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