A hat-trick by Rijeka's Leon Benko virtually ended Prestatyn Town's European adventure in the second qualifying round, first leg.
Croatian international Benko struck twice in the opening period and once after the break.
Vedran Jugovic and Damir Zlomislic added late goals for the hosts at Stadion Kantrida.
That left the Welsh Premier part-timers facing an uphill task ahead of the second leg on Thursday, 25 July.
Prestatyn went into the game having provided the Welsh highlight of the previous round by beating
And they started brightly in Rijeka only to behind after 19 minutes with Benko slotting home from five yards following good work down the right from Josip Brezovec.
Benko doubled the home side's advantage with a close-range header, again set up from the right hand side.
The Welsh side fought to get back in to the game with Ross Stephens spurning their best chance, shooting wide on 26 minutes.
But the hosts continued to have the better chances and the visitors were fortunate to be trailing by just two goals at the break.
Rijeka's superiority told in the second period as Benko completed his night's work in front of goal.
Jugovic and Zlomislic provided the finishing touches that underlined the gulf in class between the teams.
VIEW FROM PRESTATYN TOWN
Prestatyn captain David Hayes told BBC Radio Wales: "We knew we were up against it anyway, but coming here realising the international players they've got, we just knew…
"We were hoping basically that if we could keep it tight for maybe 10-15 minutes, which we did, and we were really disappointed to concede a second goal… after 20 minutes.
"But like I say, a really good team like that, you've got to expect to be switched on… because they were switched on in everything they did.
"They were clinical in everything they did. They don't really make mistakes either."