"We started off like a house on fire and I felt we coped pretty well with what Glasgow threw at us. It was another game in which we grew up," said Turner.
"There were a couple of boys who didn't train in the week but they still got through most of the game. That's the attitude we want from this squad and we're very pleased.
"European competition has told me that good sides take something away after spending time in the opposition 22. I am pleased with that aspect of our play. All in all there were some tremendous performances out there. The pack as a whole, (Rory) Sidey and (Marc) Stcherbina in the middle and (James) Arlidge who kept knocking the points over for us. Bath will be another challenge for us next week.
"All in all, this has been another step forward for us".
His sentiments were echoed by Dragons captain, Luke Charteris.
"We'd identified certain areas of the Glasgow lineout to exploit during the game which we did well. Hopefully we can look at some videos of Bath now to use for next week.
"I've been living in Bath for the last seven years now but next week will be the first time I've had the opportunity to play against them and I'm looking forward to it. It's our aim in the Heineken Cup to win our home games but it's up to us to continue our good form going into next week against Bath".