Having finished two over thanks to an opening round of 73 on Thursday, Aberg shot rounds of 67 and 68 on Friday and yesterday, respectively, to go into the final day on -5, nine shots off the lead.
The world number nine was going to need a lot to fall his way on the final round, but he was giving himself every chance with three birdies and a solitary bogey on the front nine.
However, the 25-year-old's hopes collapsed early on the back nine, as he scored a triple birdie on the par-five 11th hole to leave him one over for the day.
Aberg put that mishap behind him with consecutive birdies, but in the end only a birdie on the final hole ensured he finished the round under par.
-1 for the day ensured the 2024 Masters runner-up finished on -6 for the Open, which at time of writing sees him sitting tied for 23rd, with several players still out on the Country Antrim course.
In the end, Aberg was not enough the top Swedish entrant in the championship, as he finished a shot behind Jesper Svensson.
The world number 135 capped off an excellent week with a -5 final round of 66, his best of the championship, to finish on -7.
Former Open champion Henrik Stenson will finish the 2025 edition tied for 45th on -1 after a level par final round, while Sebastian Soderberg will finish last of the 70 players who made the cut midway through the tournament, as he posted a six over round of 77 to finish on +11.