The Devon outfit narrowly lost 24-21 at Northampton Saints having surrendered the lead following a late first-half comeback.
Cheifs did manage to earn a bonus point after Matt Jess's try, but Baxter says that he is frustrated by the loss.
"I'm not too disappointed, I'm more frustrated than anything," said Baxter. "We were in a tough Premiership game of rugby today and we were right in it until the very end. Yes we've come away with a losing bonus point for our efforts, but I was also frustrated with a couple of things we did.
"At the start we did things which we said we weren't going to do, like kicking away our first two pieces of possession, which is what you don't do against Northampton and give them the start points they wanted. But once we got that out of our system, we looked a good side, we did what we said we were going to do, and we kept the game fairly fluid and with good tempo.
"As I said, I'm frustrated with certain aspects of our game, but on the whole I'm pretty pleased with the majority of our play. We have come to Franklin's Gardens twice in the Premiership before and the truth is although we got a losing bonus point in the first meeting here, last season we were well beaten and ended up on the end of a 33-3 scoreline."
Next up for Chiefs is a trip to London Welsh on Sunday.