Neath suffered defeat on their Europa League debut despite Lee Trundle giving them the lead in Norway.
The former Swansea striker opened the scoring with a free-kick on 23 minutes.
Aalesund were level on 35 minutes through Lars Fuhre before Magnus Sylling Olsen gave them the lead two minutes later.
Three minutes into the second half, Fredrik Ulvestad scored from the penalty spot for the hosts before a fourth from Kjell Rune Sellin.
Neath manager Terry Boyle, in his first competitive game in charge, said he was proud of his side's efforts despite defeat in the first qualifying round match.
"[It was] great experience for the club, great experience for the young lads in the squad and hopefully we'll learn and benefit from it," he said.
"Obviously I've got to take the plusses out of it and be upbeat with the performance we put in. From our point of view we'll take a lot of plusses out of it."
Aalesund: Sandqvist, Jaager, Tollas, Arnefjord, Parr, Morrison, Fredrik Ulvestad, Michael Barrantes, Okoronkwo, Olsen, Fuhre.
Subs: Grytebust, Skiri, Skagestad, Larsen, Phillips, Sellin, Flotre.
Neath: Kendall, Hillier, O'Leary, Harris, Lewis, Jones, Fowler, Bowen, Collins, Morgan, Trundle.
Subs: Nicholas, Rees, Hughes,Cooper, Thomas, Cummings, Preen.
Referee: Domagoj Vuckov (Croatia)