The Dons started their Europa League campaign in style with a convincing win in the first qualifying round but it came at a price with Peter Pawlett limping off with an ankle knock after he was kicked off the ball by Giedrius Tomkevicius.
Aberdeen were one up through Shay Logan's header when Pawlett went off just after the break and they took command as Adam Rooney's double and goals from Niall McGinn and Jonny Hayes took them clear.
The visitors had two men sent off and a further five booked by French refere Nicolas Rainville and McInnes was relieved his side remained disciplined.
"The players' approach allowed us to have control from start to finish," he said. "We scored some good goals, we should have probably scored more.
"We had plenty of shots but I can't praise the players more because that's the reward for their hard work during the close season, and the work they put it in during pre-season.
"They were ready to play at a tempo that made us difficult to play against.
"The game ran away from them, they lost their discipline, and I was just glad to get off the pitch without any more injuries.
"I thought the referee tried to keep a lid on it, the officials did well. We just tried to concentrate on finding ways to break them down."
On Pawlett, McInnes said: "His ankle has thickened up with swelling, we will see how that responds in the next few days."