Ian Whitten added a sixth following the break before the Blues threatened a comeback and salvaged a try-scoring bonus-point of their own.
"I didn't envisage it would go that well," said Baxter.
"At the end of the day we played some exceptional rugby in the first half but I'm obviously still recovering from that second-half.
"It was a big performance from the players. We did exactly what we said we were going to do.
"We carried on our last performance from Gloucester and some of our best rugby this season in that first period.
"But we're sitting here a bit disappointed that we have given Cardiff Blues a bonus-point after a couple of yellow cards."
The emphatic victory sees the Chiefs soar to the top of Pool Two and Baxter admits it puts his side in the perfect position ahead of next week's away clash with Glasgow Warriors.
"Five points will do us well in the first round of the Heineken Cup," added Baxter.
"We're prepared to say where we end up in the pool is what we deserve and we will take it on the chin. What we want to do is perform each week like today.
"Go out there, give it our best shot and stick to the rugby we want to play. If that brings rewards fantastic, if it doesn't then at least we're trying to do what we want against the best teams in Europe.
"Today puts us in a good position and everything is to play for next week. We'll try to hit the pitch in Glasgow in the same way as we did today."