The Black Cats found themselves on the back foot inside the opening minute at Arsenal on Sunday, with Robin van Persie breaking the deadlock after just 29 seconds.
Steve Bruce's side were able to pull themselves level through Sebastian Larsson's spectacular free-kick, but were then guilty of wasting a number of opportunities before seeing van Persie lash home late on.
A disjointed showing in north London arrived on the back of a 2-2 draw with West Brom before the international break that saw the Baggies take a two-goal lead inside five minutes.
Turner forms part of a back four that has been caught napping too often this season and he concedes the mistakes need to be eradicated if Sunderland are to pull away from the lower reaches of the Premier League table.
"It's a big game now for us on Saturday and we go to Bolton needing to put in a performance, like we did for periods of yesterday's match," he told the Sunderland Echo.
"I'm sure we can and then we'll start getting results. Before we went out yesterday, we said that we needed to have a good start and keep them quiet.
"It's bitterly disappointing to concede so early in the game - that can't keep happening.
"We need to put that right straight away, starting with Bolton."
Turner believes the Black Cats were unfortunate to leave the Emirates empty-handed over the weekend, having seen Jack Colback and Lee Cattermole go close after Larsson's leveller, but admits they ultimately shot themselves in the foot.
He added: "We feel like we could have won the game, certainly after the first half when we weathered the early storm. We played some good stuff and created the best three chances of the game.
"We were disappointed we didn't come in leading, although we'd have probably taken a draw going in after the first 20 minutes.
"It was a wonderful free-kick from Seb. Everyone knows he's capable of that and we created a couple of good chances that fell to Jack and Catts. It's disappointing we couldn't put one of them away.
"In the second half, we knew they'd have more of the possession, but we were fairly comfortable in terms of them creating chances.
"We restricted them to long-range efforts and a few free-kicks, one of which we've eventually been undone by. We said during the second half that we needed to stop giving away the free-kicks before they put one in the top corner.
"It's obviously disappointing that we've come away with nothing."