The Dons failed to capitalise on a series of chances - which numbered double figures before half-time on Thursday night - before Milivoje Novakovic stunned the hosts with a smart finish in the 83rd minute from what was the Slovenians' second real opportunity of the third qualifying round first-leg tie.
But Jonny Hayes slotted home four minutes later after good hold-up play from Adam Rooney and McInnes feels the 1-1 draw - and the manner of their performance - should give them ample hope.
"First and foremost, I'm delighted with the response of the players," McInnes said.
"Clearly when we went behind, it was really sore on them because we were the better team throughout, created the better chances, played with the better intensity.
"We tried to get the balance right of being the team that asked questions, got crosses into the box and really gave them something to concern themselves with.
"We did all of that apart from getting the goal. We created umpteen opportunities, got in good areas, but I think they had one chance in open play and took it. That's the quality they have.
"We are a bit annoyed with the goal but rather than feeling sorry for themselves, the thing I'm thinking about most is the response of the players. It's been similar throughout this season with the late goals.
"One goal might be enough to make sure there's something to play for over there. There's no doubt Maribor are in a stronger position but we scored three goals last year in Rijeka, we scored two goals the year before in Groningen. We can score over there.
"The players will know they can score as well after the way they performed.
"They are very compact and don't lose many goals but they will remember what they faced tonight and they will be aware we can get to them. The plan is to get them again next week.
"If we create even a quarter of the chances we created tonight, I'm confident we have players who can take those chances. They will know they have work to do to get through the tie. We rattled them, but we are respectful of their quality."
Source: PA/Aberdeen FC YouTube Channel