Aalesund score twice to send Neath out of the Europa League, the Welsh side losing 6-1 on aggregate.
Neath went into the tie 4-1 down following the first leg and the Eagles fell further behind in the 53rd minute at the Gnoll when Michael Barrantes struck.
Aalesund completed their progress to the second qualifying round when Magnus Sylling Olsen hit home in the 79th minute.
Olsen also scored in the first leg.
Neath: Kendall, Hillier, Lewis, O'Leary, Rees, Collins, Fowler, Hughes, Trundle, Bowen, Harris.
Subs: Nicholas, Jones, Cooper, Thomas, Cummings, Preen, Morgan.
Aalesund: Sandqvist, Skiri, Skagestad, Jalasto, Olsen, Larsen, Parr, Arnefjord, Phillips, Okoronkwo, Michael Barrantes.
Subs: Grytebust, Myklebust, Sellin, Flotre, Sandnes, Fredrik Ulvestad, Fuhre.
Referee: Christof Dierick (Belgium)