The Dons took a comfortable 3-0 lead into the second leg at home against the Croatian side after an excellent victory abroad last week.
They seemed to be easing into the next stage too after a goalless first half but suddenly found themselves on the ropes after conceding twice in a five-minute spell after the break.
The Scottish Premiership side responded well, however, and hit back within seconds as Niall McGinn scored to provide breathing space.
Jonny Hayes then levelled on the night to restore the three-goal cushion and seal a meeting with Kazakh side FC Kairat in the penultimate preliminary phase.
McInnes said: “It was an anxious evening for a minute. When the second goal went in the momentum was with them and they started to believe.
“We always knew if we scored what they would require would be too much and at half-time we were pleased with what the players had given us.
“No-one will test our discipline domestically like that and their movement and swiftness of their play was excellent. They really tested us but we handed it and created enough chances.”
McInnes expects another difficult tie against Kairat in Kazakhstan, which will involve an 8,000-mile round trip for the first leg on Thursday Julty 30.
He added: “We’re just over an hour to China, so I’m told, We’ll have them watched on Sunday. They’ve got their last game on Sunday before the split and have only lost 13 goals in the league this season.
“They don’t find goals hard to come by either and it will be a tough ask but we expect that at this stage. They will know they are getting a tough team at this stage of the competition too.
“The distance makes the tie a bit more complicated but we’d rather be in it than watching others. We’ve worked so hard to have nights like this and we are determined to have a few more.”