Lechner sent off Dons midfielder Funso Ojo for two bookable offences in the first 20 minutes with Rijeka scoring either side of his dismissal to put the tie beyond the home side’s reach.
The team from Croatia will now face Gent of Belgium for a place in the group stage. For Aberdeen, it is the sixth successive season that they have failed to progress beyond the third round of qualification in this competition.
The Aberdeen manager had hoped a balanced approach in attack and defence would see them overhaul a 2-0 first-leg deficit, but they were naively picked off twice on the counter-attack although McInnes is convinced unjust refereeing was equally culpable in the defeat.
“It’s unusual to see a red card after 20 minutes,” he said. “I saw some tackles from our opponents and it wasn’t even a yellow card. I found it really bizarre how he can show Funso a red card in that situation.
“The game is done when we go down to ten men. Everything before that is what we need to analyse. Anything after that is unfair on the team.
“We wanted to be measured and go and ask the question. We never gave ourselves a chance. We were guilty of losing possession too easily.
“We didn’t show that confidence and experience. We made some poor decisions. The team was right and I felt they could get the job done but we never gave ourselves a chance."
Rijeka manager Igor Biscan admitted the game was more like a training match after their two first-half goals either side of Aberdeen midfielder Funso Ojo’s early dismissal for two yellow cards.
The former Liverpool midfielder was delighted to see his side score with quality counterattacks and revealed he wasn’t deceived by Aberdeen’s claim that top scorer Sam Cosgrove would miss the tie through injury.
“I told you that I wasn’t really hoping he wouldn’t play,” said Biscan. “He’s one of the most important players in their team.
"But, if you want to go through, you need to be ready for anything. I wasn’t that surprised. Everybody was telling me he wasn’t going to play. In the end, it didn’t make any difference. Our team won.”