Mark McCall said Saracens "suffocated" Exeter Chiefs in the Premiership final after a victory he said was built on experience.
The Lions overcame South African rivals Stormers 41-22 in an exhilarating Super Rugby clash in Johannesburg.
Lyon booked a Top 14 semi-final against Clermont after a hard-fought 21-16 victory over Montpellier on Saturday.
Exeter Chiefs led by 11 points midway through the second half, but Saracens produced a comeback worthy of champions to win the double.
The Crusaders were 20-0 up midway through the first half, but the Chiefs rolled up their sleeves to pull off an unlikely victory.