Baxter's team ran in four tries and exposed the defensive frailties of Wasps, whose own hopes of playing in Europe's premier club competition next season were wrecked by their seventh successive defeat in all competitions.
Baxter said: "We showed an enthusiasm and an endeavour when we were points up which we have sometimes lacked and we kept at them."
He added: "Physically it was a pretty tough game because we had such endeavour to carry the ball so much and play so much rugby.
"Attacking-wise we got a lot right today. Whether they ran into a brick wall or found space, they got up again and carried again and that was the key to the game.
"Ultimately, that created enough momentum and enough space for us to find some holes, which we did very well.
Baxter revealed that there was no pressure from the club to secure Heineken Cup rugby.
"It's important to the players but it's not the be all and end all for Exeter rugby club," he said.
Wasps coach Dai Young said: "It was evident that defensive lapses, people struggling to get into position and not making first-up tackles cost us.
"Credit to Exeter, they are a good side but they didn't bring anything we didn't expect. I felt today that a lot of senior players fell off a lot of tackles which you would expect them to make."
- Sports & Recreation