The home side dominated for the majority of the first half without really troubling Brian Maher in the Derry City goal.
Niko Jankovic, Branko Pavic and Mladen Devetak all blazed over for the hosts, who struggled to have any real cutting edge despite controlling the ball.
Derry failed to really impose themselves on the game until the final five minutes of the half, and were unlucky not go in leading at the break.
Michael Duffy's effort from inside the area looked destined for the bottom corner of the net, only to be deflected wide at the last.
Rijeka hit the front early in the second half, with Fruk firing past Brian Maher when punishing a momentary lapse of concentration in the visiting defence.
The home side really should have doubled their lead moments later as debutant Brooklyn Lyons-Foster cleared Daniel Adu-Adjei's effort off the line before Brian Maher saved Tiago Dantas' follow-up.
Derry went on the front foot after a triple substitution.
Adam O'Reilly surged forward on the counterattack before delivering a delightful cross into the box towards Michael Duffy, who was poised to head home. However, goalscorer Toni Fruk was on hand to produce an acrobatic clearance, denying Duffy at the vital moment.
Justas Lasickas missed a glorious chance for the Croatian side in injury time, as Rijeka had to settle for a one-goal advantage before the return leg at the Ryan McBride Brandywell next week.