Scott McDonald and Shunsuke Nakamura teamed up for the goal

"They will be disappointing not to get something out of the game," he said.

"Fair play to them, they were right in our faces and we found it difficult to get our key players into the game.

"But it's a good sign when you do not play well but get results. We are in a title battle with Rangers and need to grind out results."

Interview: Celtic manager Gordon Strachan

McDonald shrugged off television evidence that suggested he had been offside when heading the winning goal in first-half stoppage time.

"Sometimes you get them, but I seem to remember that at Inverness I was not offside and didn't get the goal," he said.

If Nakamura had not been there, it would have been a draw Celtic manager Gordon Strachan

McDonald paid tribute to midfielder Shunsuke Nakamura, who had otherwise looked off the pace as he continues his comeback from injury.

He described Nakamura as "a magician" following the cross that created the goal.

Manager Gordon Strachan also praised Nakamura while admitting that the player who was substituted late in the game had not put in his best performance for the club.

"If he had not been there, it would have been a draw," he said.

Strachan was relieved to come away with three points.

"That was hard work, the conditions were not great for playing football and we didn't play the right way for the first half-hour," he told BBC Sport.

MY SPORT: DEBATE Celtic were as poor today as I've seen them in long and many a day JosiahEdwardBartlet

"We adjusted things after that and it got better.

"We tried to play an expansive game, but it is a lesson that we can't do that on a pitch like that when it's windy."

But Strachan pointed out that the most important thing was the victory.

"We had players who were not at the top of their form," he said.