A decent opening 10 minutes failed to produce a clear chance for either side, but Juanfran then came close for Betis, cutting in from the right before powering a shot at goal.
The home side pressed again, this time through Salvador Lopez Sevilla. The midfielder was played in, but he put his effort wide with just Ivan Vargic to beat.
Rijeka should have made them pay for that miss, but Leon Benko was guilty of missing an open goal from six yards out with a header.
Juanfran then fired a shot at Vargic, before the visitors went up the other end and Zoran Kvrzic blasted over as the poor finishing continued.
In the second half clear-cut chances were at a minimum, with Betis seemingly content to slow down the tempo.
Benko had an effort from 30 yards well saved by Guillermo Sara, and after that the home side began to up the ante, but were unable to find a winner.