The Devon outfit earned many plaudits despite losing their opening game 9-6 at defending champions Leinster on Saturday and face French giants Clermont Auvergne this weekend.
The Chiefs progressed to the last eight of the Amlin Challenge Cup last year after winning all of their group matches at Sandy Park, and Baxter knows that his side are going to have to try their best to repeat that achievement.
"The challenge is for the players to show the same level of intensity as last week and make sure they perform at home," said Baxter. "Every cup competition that has this pool stage element is massively built around how you perform at home.
"We've done a decent job in going to Leinster and getting a losing bonus point but that only really becomes of any worth for us if we perform well this weekend.
"The important thing for me now as head coach is to make sure everybody's feet stay on the ground. That's the first time we've done it, now the challenge is can we do it again, and again and again. That's what good players do, they don't just do it once off but again and again."
Chiefs currently sit sixth in the Aviva Premiership table.