"It was hard work," he admitted to BBC Scotland.
"We didn't play the right way for the first half-hour, so we're delighted to get a win."
Japanese playmaker Shunsuke Nakamura was a peripheral figure in a tight game until his fine cross was headed home in first-half injury time.
"Give it to Naka. He found it difficult today with the wind and the bumpy surface, but he can produce a moment of magic. Scott (McDonald) got a lovely header on it."