The La Liga outfit led 1-0 in Croatia on Thursday thanks to Iago Aspas' first-half strike.
French defender Timothee Kolodziejczak was sent off seven minutes into the second half, though, and Andrej Kramaric tucked away the resultant penalty.
Rijeka looked winners after Zoran Kvrzic put them in front in the 68th minute but Stephane M'Bia came off the bench to spare Sevilla's blushes with an injury-time equaliser.
Emery is quoted as telling AS: "We knew it would be a tough match.
"We had the game under control and knew we had to wait for our chance to get the second but the penalty and red card changed the game.
"With one less [player] we wanted to remain strong and we did ... the team has worked hard but has failed to attack dangerously enough.
"We are not happy but this has to give us optimism for improvement."
Sevilla still top Group G with four points from two matches.
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