Hibernian came close to knocking Brondby out of the Europa League, only to lose 5-3 on penalties after it finished 1-1 on aggregate.
Hibs had lost 1-0 at Easter Road in the first leg of the second-round qualifier but Scottish Cup final hero David Gray scored the only goal of the return match in Denmark.
Neil Lennon's side were bidding to set up a meeting with Hertha Berlin but John McGinn was the only player to miss in the shoot-out as Brondby progressed.
Hearts suffered a shock 2-1 home defeat to Birkirkara, having drawn the first leg 0-0 in Malta. Prince Buaben missed a first-half penalty before the visitors scored twice in the second half. Connor Sammon got one back for Robbie Neilson's men but it wasn't enough.