Despite a dominant display which included three tries from David Ewers, Myles Dorrian and Ally Muldowney, the Chiefs were unable to take maximum points, although their LV= Cup semi-final hopes remained alive.
Baxter said: "Any win against Premiership opposition is a good one, but we're a little disappointed that we couldn't force through the bonus point.
"But at the same time, we've come here with a completely different team, scored three tries and before their score at the end looked like we weren't going to concede any.
"I'm pleased with the performance overall and with the performances of a number of our individual players.
"But we had plenty of time to go for the fourth try and maybe we hunted it in the wrong way and we started to get carried away and lose control of the game.
"We were trying missed passes or little off-loads and made some poor decisions that broke the play up."
Exeter took control of the match as Ewers crashed over before Pat Phibbs sent Dorrian in under the posts.
Muldowney scored their third try early in the second half but the fourth wouldn't arrive and Wasps scored a late consolation through Mike Powell.
Wasps forwards coach Trevor Woodman said: "At half-time, we wanted to get some field position and score first but that didn't happen and we came under a lot of pressure again.
"One thing that we consistently ask is that these boys stick to it and to see that late rally was good, with a few of our young kids coming on showing what it means to them.
"We've got to get into the position now where we're more clinical and make sure the opportunities that we create get finished off.
"The side that played against Bordeaux last week have all been given the week off and it was a good opportunity for new signings and guys coming back from injury to come in and get the shirt on."
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