Substitute Jayden Stockley was sent off for two bookings within 10 minutes of his introduction from the bench and the Pittodrie side had a goal disallowed.
They also missed a penalty and scored an own goal as the Slovenian hosts won 1-0 to reach the play-off round.
"The officials played the biggest part in the defining moments," McInnes said.
Striker Stockley was dismissed midway through the second half - with the game goalless - after being booked twice for aerial challenges.
"The sending-off was ridiculous. I don't think you see that in any other country - two yellow cards for that. Stockley's just trying to use his arms for leverage.
"Right from the outset he [the referee] blew his whistle at the slightest moment of contact."
In the first half, striker Adam Rooney was fouled by goalkeeper Jasmin Handanovic when clean through on goal.
The ball broke to Niall McGinn, who rolled into the unguarded net, but referee Popov opted to award a penalty and book Handanovic, who then saved Rooney's effort.
"He was very quick to blow for the penalty kick," McInnes said of the referee.
"Games are decided on key moments but you could say the Rooney penalty miss was defining but we still have to overcome the officials.
"The goal should stand. The new rules suggest that the double whammy of the penalty and the red card has changed now so I wasn't against that decision.
"I can't remember Rooney missing a penalty. It's very unlike him but we don't apportion blame or criticism to him."
McInnes was keen also to absolve goalkeeper Joe Lewis after Graeme Shinnie's pass-back bobbled over his foot and rolled into the net for Maribor's winner.
"It's a horrendous bobble," McInnes said. "It's come up six inches off the ground. You can't do much about that."
A minute's silence preceded the match after two players from Maribor's B team - Damjan Marjanovic and Zoran Baljak - died in a car crash earlier in the week.
"We credit Maribor," added McInnes. "It was a difficult evening for them in the circumstances.
"The result was very harsh. My team showed tremendous courage, fight, ability, intelligence and, over the two games, we deserved more, but such is football."
Manager Derek McInnes criticised referee Nikola Popov and his assistants following Aberdeen's 2-1 Europa League aggregate defeat by Maribor.