Turner said: "Naturally the pre-season matches have given us a boost but they count for nothing now we are entering the competitive stage of the season.
"We have a difficult start to our league campaign with three away matches so our feet are firmly on the ground despite last Saturday's result. We need to get some away wins if we are to be competitive in the league."
Turner has announced a 24-man squad for the trip to Scotland including ex-Glasgow flanker Andrew Hall, who looks set to make his competitive debut for the Dragons against his former club.
Turner added: "The good thing is we know how to win at Glasgow but we are aware of the challenge they pose and are not underestimating them in the slightest."