Rob Baxter is not putting a timescale on how long Jack Nowell will be out, but does not believe he is a Rugby World Cup doubt.
Munster, Racing 92 and the Ospreys will take on holders Saracens in the pool stage of the 2019-20 European Champions Cup.
Mark McCall said Saracens "suffocated" Exeter Chiefs in the Premiership final after a victory he said was built on experience.
Exeter Chiefs led by 11 points midway through the second half, but Saracens produced a comeback worthy of champions to win the double.
Northampton Saints took the final Premiership play-off spot despite losing to Exeter, while Bath secured Champions Cup rugby next term.
Having spent six successive years in the top flight, Newcastle Falcons were relegated from the Premiership on Saturday.
Exeter Chiefs and Saracens kept winning at the top on Saturday, while Leicester Tigers' Premiership status is not yet secured.
With Ollie Devoto's try against Harlequins on Saturday, Exeter Chiefs crossed in a record 72nd consecutive Premiership match.
A bonus point and a piece of history made it the happiest of Sunday's for Wasps, who defeated Exeter Chiefs 26-19 at Sandy Park.
Exeter Chiefs earned a home semi-final with four games to spare, while Saracens scored a late try to hurt Newcastle's survival hopes.