However, a fourth try would have gifted Chiefs a bonus point and while Baxter is pleased with his team's display, he can't help but feel that Exeter should have taken five points from the game.
"It was four very valuable points but I can't help but feel that we left a point out there, not least because large parts of our game held up well and should have given us a foundation to push on a little earlier than we did," said Baxter.
"The enthusiasm of the players to defend was far better than last week at Bath. Our toughness on the game line in the first half was better than last week and our maul defence was fantastic.
"You have to give Worcester credit, they are a good dogged side and they are not just going to give up on the game."
Next up for Chiefs is a trip to Aviva Premiership new boys London Welsh on Sunday.