Aberdeen kicked off their Europa League campaign in style with a convincing 5-0 win in the first qualifying round but it came at a price with Peter Pawlett limping off with an ankle knock.
The visitors had two men sent off and a further five booked by French referee Nicolas Rainville and McInnes was relieved his side remained disciplined.
He said: "The game ran away from [Daugava], 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."
Source: Sky Sports