Peter Pawlett limped off with an ankle injury after some bruising treatment from the Latvians, who had two men sent off in the course of their 5-0 defeat.
Pawlett's fitness will be assessed in the coming days but he might be rested for the formality of the second leg in Riga next Thursday. McInnes praised referee Nicolas Rainville and his assistants and was diplomatic about Daugava, but said their rough tackling worried him. "They lost their discipline and I was just glad to get off the pitch without any more injuries, to be honest," he said.
"I thought the referee tried to keep a lid on it and the officials did well. We just tried to concentrate on finding an answer and ways to break them down. The last couple of goals were very important to us and very pleasing.
"I don't know how Peter is, his ankle has thickened up a wee bit with swelling. We'll see how that responds in the next few days. But you see what he gives us - in that 45 minutes he was on he was electric at times - so hopefully he will be okay.
"I think there was a lot of frustration from their point of view about how the game was going. There were a few late challenges going in, reckless challenges, but I thought the referee dealt with it well as a whole.
"We just wanted to try to concentrate on our own performance and keep our level of discipline, which we stressed to the players was vital in European competition. They could possibly have had more players sent off but thankfully we're not talking about that.
"It was a professional performance," he added. "The players' approach to it allowed us to have control of the game from start to finish. We scored some good goals, we should probably have scored more. We were a bit wasteful at times, on another night maybe we would have a few more going in. But I can't praise the players enough.
"That performance was the reward for them being ready to play tonight, the reward for their hard work in the pre-season. They were ready to play at a tempo tonight. We have to be professional in the second leg and approach it the same way."
Adam Rooney scored twice and Shay Logan, Niall McGinn and Jonny Hayes got one each as Aberdeen set up a second-round tie against Groningen.