The Devonian outfit moved up to sixth in the Aviva Premiership with one match remaining this season with a 37-24 win over Wasps on Sunday.
Exeter would earn a place in the Heineken Cup should they finish in their current position, but Baxter was keen to take that pressure off of his players.
"Physically it was a pretty tough game because we had such endeaour to carry the ball so much and play so much rugby," Baxter told BBC Sport. "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. We showed an enthusiasm and an endeavour when we were points up, which we have sometimes lacked, and we kept at them.
"It (qualifying for the Heineken Cup) is important to the players but it's not the be all and end all for Exeter rugby club. It's great for us - we get a couple of big gates, and the performance you saw there was from a group of players who want to be in the Heineken Cup and achieve."
Chiefs host Gloucester in their final match of the campaign on May 4.