IT would be a distortion of the facts to say everyone went home happy at the end of the resumption of ancient hostilities in Glasgow, but there was a clear sense that both tribes were able to live with how the League Cup semi-final unfolded at Hampden.

Celtic earned the cup final place their superiority merited and Rangers were spared the mauling which seemed to be coming to them after Leigh Griffiths and Kris Commons opened them up with goals in the first half an hour.

Some Celtic fans nursed mild frustration over the humdrum winning score - opportunities to bury a clearly inferior Rangers don't come around every week - but all they showed was pleasure as they enjoyed their team's half-lap of honour at full-time.

They enthusiastically roared approval when Ronny Deila did his usual celebration routine. The day was a quietly successful one for a manager under pressure to avoid an unthinkable defeat.

That it finished 2-0 allowed a limited Rangers team to maintain its dignity. There was no humiliation for them, and it will not be remembered they barely laid a glove on Celtic even after offering more in the second half than they had during a first 45 spent constantly on the retreat.

Celtic worked themselves into a winning position and then went off the boil. It made for a generally uneventful Old Firm game in the end, not helped by a playing surface which looked poor at kick-off and deteriorated as the day wore on.

Five bookings, and no red cards, was evidence that both sets of players largely heeded all the warnings dished out to them about behaving responsibly.

Some laughable guff was spouted in the days before the game about how reports of this or that comment could be "pinned on the dressing room wall" by Rangers as motivation. It was laughable because motivation was always going to be the least of Rangers' worries.

Kenny McDowall had Kyle Hutton, Nicky Law and Ian Black in the middle. None of them were up to the job of containing Celtic in the first half, when the game was won.

Their reactions, movement and decision-making were too slow and ponderous, not only at the Celtic goals but in the general flow of the game. Black was on his backside, complaining, three times in the opening minutes.

Fraser Aird and Steven Smith, Rangers' other midfielders, offered nothing from the wings and all of it meant Kenny Miller was inevitably an isolated, irrelevant figure up front. There was no threat to the Celtic goal bar some hopeful punts at corners and free-kicks, all of which Craig Gordon calmly gobbled up. All over the pitch Celtic were sharper and far more purposeful.

Mikael Lustig took a throw to Stefan Johasen. No Rangers player went to him, giving him the time and space to deliver a good ball to the far post. Either Darren McGregor or Richard Foster could have won it but neither did and Griffiths leapt between them to score a wonderful header.

The second was another exploitation of Rangers' failings. Challenges by Law and Black on Scott Brown were pitifully soft at the edge of the box. Law did at least get get a foot on he ball but only hooked it straight to Commons, who rifled a superb rising shot high into Steve Simonsen's net despite the goalkeeper getting a hand on it.

Deila had asked for controlled aggression from his team, and that was what he got. Griffiths was booked for cupping his hand behind his ear as he celebrated his goal and Lustig got one for a foul on Smith.

But Celtic's drive was focused and controlled. Their hunger was illustrated in Brown's angry, frustrated reaction when referee Craig Thomson failed to play advantage when Griffiths was clean through, instead recalling play for a foul by Black. Had Grifiths been allowed to carry on and converted the chance Celtic would have been 3-0 up in 34 minutes.

Virgil van Dijk passed up another chance with an awkward header over the bar from a corner. Celtic were snapping at Rangers. Griffiths robbed a sleeping McGregor, Commons beat McCulloch in the air and no-one tracked a terrific Johansen run into the box which might have brought another goal. Celtic won individual battles all over the pitch.

Rangers still sat deep, still had 10 men behind the ball, even at 2-0 down. It was going down as a tame surrender although they offered plenty of spirit in the second half when Jon Daly came on for Aird. The shape was tweaked, 4-4-1-1 with Miller withdrawing slightly deeper, and they won more tackles and saw more of the ball as Celtic lost their rhythm.

Rangers couldn't get anything to show for it, although Lee Wallace did float a chip just over the bar, but it gave their defence a welcome relief. The game became bitty and fractured, with niggly fouls constantly breaking up any flow.

Challenges were spiky rather than wild. Tempers were generally kept in check although there was a brief melee after Brown went scything through Black in stoppage time.

"Broonie, Broonie" chanted the Celtic support. Their captain was the man of the match. By the time of their half-lap of honour he had stripped to his waist and before heading up the tunnel he had removed his boots and handed them to a supporter.

Shirt gone, boots gone: there was hardly anything left, but on this form it was easy to imagine him wearing a League Cup winner's medal around his neck after the final against Dundee United on March 15.