The Black Cats' last three league games have pitted them against Arsenal, Liverpool and Manchester United, and while they failed to win any of them, a run of three draws nevertheless underlined the growing strength of Steve Bruce's squad.
Sunderland led for much of the second half at Anfield, and were the better side for large periods of last weekend's home game with Manchester United.
So while a return of eight points from seven matches might not sound too impressive, Turner feels it is more than satisfactory given the difficulty of the Wearsiders' start.
"We're probably a little bit disappointed we haven't won one of our last three games," said the centre-half. "But looking back, you'd take three draws all day.
"Against Arsenal, we felt we maybe should have wrapped that game up, and against United we needed to get in front when we were on top and never did.
"But to come through three tough games like that, we've got to be pleased with how we're playing and what we've achieved. The start we've made will give us huge confidence."
Coming off the back of a positive result against Manchester United, the current international break has come at something of an inopportune time for the Black Cats.
Injuries to Craig Gordon and Kieran Richardson should have cleared up completely by the time Sunderland reconvene for the trip to Blackburn on October 18, but Bruce will have to guard against a stalling of the momentum that has been generated in the last few weeks.
"It (the break) probably comes at a bad time," said Turner. "I'm sure all the lads would like a midweek game and another one on the weekend, the way we're playing.
"But it's come around and a few of the boys have played every game so far, so they'll get a bit of a rest.
"We'll still be training and working hard. The training ground's been a really good place to be around. I'm sure it'll get better next week, and we'll still have confidence in the way we're playing."
Meanwhile, Leeds United have extended George McCartney's loan by two days to enable the full-back to play in a rearranged game with Cardiff City on Monday, October 25.