His side will now be firm favourites to complete a league and cup double, having recently re-established a three-point lead over their arch rivals at the top of the SPL.

Strachan and opposite number Walter Smith were at pains to insist in the build-up to yesterday’s game – the first Old Firm derby final since 2003 – that the outcome would not affect the title race.

And despite the jubilation of winning his sixth major honour since moving to Parkhead almost four years ago, Strachan was in no mood to change his tune.

“I don’t think it will make any difference,” he said after the 2-0 extra-time win.

“All it gives is the Celtic or Rangers manager a couple of days leeway of being able to stick your head up over the parapet.

“I think everybody expected a close game and they got it. A lot of people would’ve backed extra-time – they got it.

“From where I was standing, it seemed to be an exciting game.”

He added: “What it does is tell us how hard it’s going to be for the rest of the season.

“We all know how close it was there and how determined they are.

“So if both teams have that determination, it’s going to be a close call.

Strachan appeared to win the tactical battle with Smith as both managers fielded slightly experimental line-ups at Hampden.

But despite admitting he had formulated his masterplan – which included playing Scott McDonald as a lone striker and defender Gary Caldwell as his midfield anchor – almost a week earlier, Strachan played down its significance.

“Forget tactics, it’s all about players,” he said, citing Liverpool’s 4-1 win at Manchester United on Saturday as an example.

“Both play the same tactics every week. Good players win on the day.

“There is too much spoken about that (tactics).”

Strachan’s men had the better of the game in normal time, with the otherwise excellent Scott Brown wasting a good chance and the outstanding Glenn Loovens seeing a volley cleared off the line.

Rangers went close through Kyle Lafferty and Nacho Novo before Darren O’Dea became Celtic’s unlikely hero by nodding them in front early in extra-time.

Aiden McGeady, a menace all afternoon, wrapped up the win from the spot in stoppage-time after being felled by Kirk Broadfoot, who was sent off.

In between those goals, Celtic missed more than one opportunity to add to their tally and Strachan admitted he feared the worst.

“Every time we missed a chance, I thought, ’Here we go’,” he said.

Rangers were forced to play Broadfoot at centre-half after losing Madjid Bougherra to injury.

But despondent manager Smith said: “I don’t think it had a great influence on the game.

“I felt Kirk Broadfoot handled himself very well in the match so I don’t think that had anything to do with the overall result.”

He added: “The game itself was one of those where we never gave ourselves an opportunity to get started in extra-time.

“You can’t blame any of our boys. Both sets of players put a lot into the game.

“I’ve got no complaints about anything any of our players did in the match.”