"It's been a tough week, probably the toughest of my career," said recently-crowned Magners League Coach of the Year Turner.
"The coaching staff have been beating themselves up and in turn we have been beating up the players. We needed a few big players to stand up and I felt the likes of Gavin Thomas, Wayne Evans and Robin Sowden-Taylor did that."
In an impressive first half, the Men Of Gwent raced into a 23-3 lead thanks to the kicking of Jason Tovey and replacement Matthew Jones, and close range tries by Robin Sowden-Taylor and Aled Brew.
But in a scrappy and ill-tempered second-half the Dragons failed to register a single point but held strong in the face of prolongued Glasgow attacks to secure their first victory of the new campaign.
"Going in 23-3 up at halftime, I didn't think it was enough but we held out", added Turner.
"We needed to score first in the second half and we didn't. We coughed the ball up too much but we played some good stuff at times.
"Our kicking out of hand was pretty poor, but the touch lines have been brought in for the stadium development and we have to come to terms with that.
"We need to limit the amount of errors we make - a better side would have put us away - but it gives us something to hang our coat on.
"We are not the same side that played good stuff last year but we will get there, that's for certain.
I'm really pleased with the players after last weekend. You always build yourself up for the weekend game and there's no doubt the players were up for it after the loss to Connacht last week.
"I'm just pleased that we got the Glasgow game out of the way and that we can come to work on Tuesday with a smile."
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