That victory ensured the Chiefs topped Pool Four ahead of Perpignan, Newport-Gwent Dragons and Cavalieri Prato. But, Wasps's bonus-point victory over Bordeaux in Pool Three on Sunday ensured the former Heineken Cup winners secured a home draw.
"We knew the various permutations going into this weekend," said Baxter.
"But the main aim for us was to make sure we beat Perpignan and get into that last eight. We did that with a fantastic win on Saturday and now our efforts have been rewarded with a great draw against Stade Francais.
"In an ideal world we would have like to have welcomed another big club to Sandy Park and the chance to play in front of our own supporters, but with Wasps winning on Sunday it means we have Stade and for us that's another great challenge.
"If I'm honest, I didn't care who we got because whoever we faced it was going to be a fantastic fixture for us. To get a draw like this is reward for the hard work and endeavour all the guys have put in, not just at the weekend, but over the course of the season so far."
For now, Baxter insists the Chiefs' focus is on the domestic front but he reckons the next block of fixtures provide the perfect opportunity to build momentum ahead of the European quarter-final.
"These next six weeks are massive for us and we will use every one of these games to get the squad up to speed and in the best possible position we can be, added Baxter.
"We will worry about Stade Francais further down the line because those other games will be the main focus for us now."
If the Chiefs are victorious in Paris they will face the winner of Toulon versus Harlequins at the end of April.