The Slovenian club has knocked Hibernian, Rangers and Celtic out of Europe in recent seasons.
Yet McInnes is adamant that his players are not fearful of the quality of the opposition or their record.
"We're not daunted by it," McInnes said. "We're confident in our ability to get the right result."
Aberdeen's manager has told fans to expect an assertive first-leg display on Thursday and urged them to back the team.
"We've learned over the last few seasons to deal with European football," McInnes continued.
"I like the technical and tactical part of it. Our supporters should expect to see a confident Aberdeen team.
"They are favourites, we're the underdogs, but we were underdogs against Riejka [last season], we were underdogs against Groningen [in 2014].
"They'll take confidence from their recent history, and not just against Scottish teams.
"We want to represent ourselves first and foremost, get the reputation of our club at the forefront of people's minds, and help Scottish football at the same time.
"Those first two rounds always have trepidation about them, because players aren't fully up to speed, they're playing against teams that are relatively unknown and there's pressure in that.
"We've now come out the other side of those ties and we're now the underdogs going into this game. I'm happy to deal with the favourites tag and happy to deal with the underdogs tag."
McInnes warns that Maribor will be accomplished and dangerous opponents in the first leg of the third qualifying round tie on Thursday at Pittodrie.
He will send his side out in search of a victory, but also with the awareness that the contest can be won in Slovenia on away goals, so keeping a clean sheet is important.
"What was telling from [Maribor's win over Levski Sofia in the last round] was their maturity and calmness, even when they went behind they kept playing their game," McInnes said.
"That comes from playing European football and they look like a team confident within their shape. They've got a way of playing, very well organised, and the refusal to panic when they went behind has got them through into this tie.
"They play 4-4-1-1, they can play a bit deeper and they counter-attack quickly. We need to be aware of that and recognise the areas where we want to play and look after the ball, especially against a team that is quick to get forward.
"We want to win the game at home, [but] it's important we still have a result going over to Maribor.
"Ideally we want to impose ourselves and get that balance between attacking and defending right, but we don't want to be giving ourselves a mountain to climb by losing goals at Pittodrie."

The four drove a vehicle into the compound in Karakax county, and set off explosives that killed one person and injured three others, they said. State media said it was a terrorist attack.
The area, predominantly Muslim Uighur, has suffered years of unrest.
The authorities blame the history of violence on Islamist militants.
Human rights and exiled Uighur groups accuse the government of repressing the Muslim community.
State news agency Xinhua did not specify whether the four people were killed by authorities on the spot or later in the day.
Last month Chinese authorities began confiscating passports from people in the region, saying it was a move to combat violence.
Uighurs, which makes up about 45% of Xinjiang's population, have often complained about having restrictions put on their freedom of movement.

The 26-year-old served a provisional 30-day suspension after testing positive for a 'fat burner' in March.
Sakho admitted taking the substance, but Uefa had to investigate whether it was actually prohibited.
Its control, ethics and disciplinary body dismissed the case after a hearing including experts from World Anti-Doping Agency-accredited laboratories.
"I am happy that this is finally over," Sakho said. "It's been a difficult time for me but I knew I had done nothing wrong.
"I am looking forward to getting back in the team and playing again."
Centre-back Sakho's failed test followed Liverpool's Europa League last-16 second-leg tie against Manchester United on 17 March.
He was eligible for selection for his country for Euro 2016 but was left out of the squad.
Liverpool said in a statement: "We are pleased for Mamadou that he can now resume his playing career."
Derek McInnes believes Aberdeen have the confidence and experience to overcome being underdogs against Maribor in the Europa League.
[NEXT_CONCEPT]
Chinese police have shot dead four people who attacked a Communist Party building in western Xinjiang province, local government officials say.
[NEXT_CONCEPT]
Liverpool and France defender Mamadou Sakho has had a doping case against him dismissed by Uefa.