Fraizer Campbell kept Cardiff in the contest in between the United goals before Kim Bo-kyung grabbed a leveller in injury-time to give the home side a deserved point.
"We played well today. We tried to press them as hard as we could. We didn't just sit in and play for a point. We tried to win the game and I think in the end, a point is about fair," Turner told Sky Sports.
"Maybe we deserved a bit more but we kept pushing and we are happy with the result."
Of his mistake in the 15th minute which led to Rooney's opener, Turner added: "I hold my hands up, I made a mistake.
"It's tough because no-one wants to make mistakes but there was a long way to go in the game and thankfully Fraizer's gone and pulled us out of the doo-doo today and we cracked on."
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