(Copenhagen win 4-0 on aggregate)
Peter Moller's class proved too much for Carmarthen
Two first-half goals in two minutes from Peter Moller ended Carmarthen's dreams of a Uefa Cup upset.
Trailing just 2-0 from the first leg in Denmark, the Welsh Premier side were eager for the rematch in Ninian Park.
But ex-Denmark international Moller coolly slotted over the advancing Tony Pennock after Michael Silberbauer's surging run and neat through ball.
Marcus Allback's clever back-heel then put the striker one-on-one with Pennock and he calmly sealed his side's win.
At half time, Carmarthen manager Mark Jones sent on striker Craig Hughes, a convicted hooligan who was only released from prison a week ago, but he struggled to make an impact.
The part-timers were more composed after the break and after 50 minutes skipper Rhodri Jones had Carmarthen's first shot, but his 20-yard effort flew over the bar.
Van Heerden had a great chance to add to Copenhagen's lead just before the hour, but Pennock blocked well.
Copenhagen substitute Peter Iseh made an immediate impact, winning a free kick which Hendre Bergdolmo curled inches over midway through the second period.
And although Copenhagen seemed to sit back and see out time, Van Heerden again tested Pennock with 15 minutes remaining.
"That was no disgrace against a top European side full of internationals," Town's proud boss Jones told BBC Sport Wales.
"There wasn't as much pressure on them as in their home leg so they played a lot better, and at times their passing was wonderful.
"At 2-0 at half-time I was fearful of a hiding, but the boys came out and did Carmarthen proud.
"We didn't create the chances we had in the first leg, but we showed passion, determination and a game plan.
"It's been a great adventure for the town and for the club."
Carmarthen: Pennock, Richard Carter, Hardy, Giles, Lloyd, Cotterall (Smothers 67), Rhodri Jones, Kennedy, Kevin Evans, Dodds (James 84), Daniel Thomas (Hughes 46).
Subs Not Used: Tucker, Warton, Burke, Walters.
FC Copenhagen: Christiansen, Jacobsen, Svensson, Linderoth (Saarinen 63), Silberbauer, Allback (Ijeh 63), Roll, Gravgaard, Bergdolmo, Van Heerden, Moller (Dos Santos 75).
Subs Not Used: Raboczki, Tobiasen, Thomassen, Bertolt.
Booked: Van Heerden.
Goals: Moller 37, 39.
Ref: Ghenadie Orlic (Moldova).