The Dons held off Rijeka's comeback from a 3-0 first leg deficit, as they drew 2-2 to win 5-2 on aggregate.
Goals from Niall McGinn and Jonny Hayes secured the draw, which helped to book a Europa League Third Qualifying Round tie against Kairat Almaty of Kazakhstan.
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 excellently and created enough chances."
The Dons manager expects a similar test against the Kazakh side, saying: "I've got three games to watch and 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."
He added: "The distance makes the tie a bit more complicated but we'd rather be in it than watching others take part
Every experience is different and European football can throw that up, but our flight is booked, we'll travel with enough room to let the players get their heads down in the flight, and we'll be ready for the game.
"We've worked so hard to have nights like this and we are determined to have a few more."
Source: PA Sport
Source: PA