Scott McDonald scored the only goal in first-half injury-time in a game played in oppressively windy conditions.

McDonald was unconcerned about the possibility that his 19th goal of the season was offside.

He said: "That's the breaks you get. I was ruled offside when I scored against Inverness and that was onside.

"It cost us the game so these things even themselves out."

Strachan told BBC Radio Scotland: "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. So we are delighted to get a win.

"We have had games where we have played some super football at Inverness and Hibs this season and not got a win."

Falkirk boss John Hughes, who watched the game from the stand while serving a touchline ban, felt his side deserved better.

"I thought the goal was offside and then we had one or two penalty claims," Hughes said.

"But once again - us getting the rub of the green or a penalty? That's me being paranoid again.

"It's disappointing, especially what the boys put into the game."

Hughes confirmed Dean Holden had broken his leg after a late tackle by Celtic skipper Stephen McManus.

He said: "It is broken, definitely one of them, the tibia or the fibula, and it could be both of them.

"It looks like he is going to be out for a long, long time.

"Deano, we will all just stick around him and wish him all the best. He'll come back from it, he's a winner."

Meanwhile, Strachan confirmed the club had signed 20-year-old Middlesbrough striker Ben Hutchinson on a pre-contract deal.

"He is something different from what we have got coming through from the younger lads," Strachan said.

"He has made his Middlesbrough debut and we could speak to him because his contract is up.

"John Park has done a lot of work on it and I have given John the go-ahead to get on with it."