After last week's first leg which Shakhtar Soligorsk won, The fixture was all square 1-1 on aggregate six minutes into the game when Michael Duffy put Derry ahead.
Shakhtar however were level four minutes later and then hit the front just before the half hour mark. By the 68th minute it was 3-1 and two goals in the last ten minutes rounded off of a Shakhtar home victory 5-1.
The final aggregate score was 6-1.
Sligo Rovers and Dundalk also bowed out of the competition on Thursday night. Sligo lost their second leg to Rosenberg 3-1 and 4-3 on aggregate while Dundalk beat Hajduk Split 2-1 in Croatia but it wasn't enough as Split progressed 3-2 on aggregate.