And while Exeter's European dream may now be over following their 22-17 reverse, Cheika is tipping them to kick on at home as they look to build on their current standing of fifth in the table.
"I reckon Exeter will make the top four because they believe in themselves," said Cheika.
"They're very well coached. Rob Baxter looks like he's very smart and he's got them very well drilled.
"When you look at them on video you can see what they do but they do it well. Even though you probably know what they're going to do, it's hard to stop.
"They've got big guys who are fully committed and you can see the core values of the Club. They've come from the second division and most of that group has stayed together. They've added a few new guys to the team and they look like they're going great guns.
"That may give them the advantage in the tight race for the play-offs."
Having already beaten French giants Perpignan in just their second season of continental competition, the Chiefs deserved to return to Devon with far more than just pride to show for their efforts a week ago.
A Sireli Naqelevuki score with a quarter of an hour remaining had looked like handing Exeter a remarkable victory but the otherwise impressive Ignacio Mieres missed the conversion and a late drop goal to leave the scores tied at 17-apiece and set up a thrilling finale in the French capital.
And although they eventually fell just short against the twice Heineken Cup finalists and last season's Amlin Challenge Cup runners up, Exeter's league form means next season's European adventure could be even more exciting for everyone at Sandy Park.