The Men of Gwent were humiliated with a 40-7 loss at Galway Sportsground in the opening round of the Magners League.
The two sides will meet again, at Rodney Parade tonight and Turner has called on his troops to make amends.
"Connacht are a good side, they proved that. We had a drubbing over there first game of the season," said Turner.
"We made all sorts of excuses after but it wasn't a good day for us, that's for sure, and we have got to try and redress the balance this week."
The Dragons and Connacht lie in 10th and 11th place in the Magners League respectively and both sides will be keen to halt their losing streaks. The Dragons have not won a game in any competition in six matches since November 26, while Connacht's losing run stretches to eight in all competitions.
But Turner can take heart from the fact that the last five clashes between the sides have been won by the home team and a three match winning streak at Rodney Parade. But he is fully aware of the magnitude of the task at hand.
"They're well coached, they've got some good structures and they've got some big forwards, so we're going to have to try and dismantle that and play our own game," added Turner.
"There's certain elements we've been improving with, it's not easy with the injuries you pick up but that's just the nature of the game these days.
"It's vital that we start chasing the pack just ahead of us, which is your Glasgows, your Edinburghs and they're within sight of us."
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