The New Saints were beaten 1-0 at Telia Parken after losing the first leg against FC Copenhagen 2-0 at home
The New Saints' opponents in the Europa League will be PFC Ludogorets Razgrad. The Bulgarian champions qualified for the third qualifying round with a 5-1 aggregate victory over Icelandic side Valur.
Saints drop into the Europa League after bowing out of the Champions League 3-0 against FC Copenhagen.
The first leg is in Bulgaria on Thursday, 8 August, with the second leg at the Racecourse ground on Thursday, 15 August.