IF there was one dampener on a joyous day for Rangers supporters, it was that this victory will spell the end for Ronny Deila as Celtic manager.

If there was one thing, meanwhile, to give disconsolate Celtic fans hope for the future, it was that there will be a new man charge at Parkhead for the start of next season.

The Celtic board have stubbornly kept faith with Deila in recent months despite a growing discontentment among their followers in the hope that he would come good.

This defeat to Rangers in the Scottish Cup semi-final suggested their admirable willingness to back their man was misplaced.

With a Rangers side that is flying under Mark Warburton set to join them in the Premiership in the 2016/17 campaign, they will now have no choice but to act and make a change.

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Celtic only lost 5-4 on penalties after the game had finished 2-2 after 120 minutes when Tom Rogic blasted his effort high over the crossbar.

But the scoreline was misleading and didn't tell the full story of the encounter. With Kenny Miller and then Barrie McKay twice giving Rangers the lead, Celtic were always playing catch-up. A victory would have flattered them.

You could argue that Deila’s side had showed great fighting spirit to level, first through Erik Sviatchenko early in the second half and then through Rogic in the second period of extra-time.

You could also suggest they enjoyed no luck. Patrick Roberts, the on-loan £12 million Manchester City winger who was one of their best performers, would have ordinarily buried the sort of glaring chance which he passed up in 33 minutes as an inviting empty net beckoned. His miss was Van Vossenesque.

The throw-in that led to the second Rangers goal – which the assistant referee Alan Mulvanny awarded to Celtic only for the match official Craig Thomson to then give to Rangers – was also contentious. But it was some distance from goal.

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In truth, Celtic were outclassed by a side put together for a fraction of the price for large swathes of the game. At no point during proceedings did they look in control. Their rivals produced superior football.

Warburton had insisted that Rangers would play their natural attacking game and he remained true to his word. Both of his full-backs, James Tavernier and Lee Wallace, got upfield frequently. Their play was a delight to watch at times.

Every one of their players turned up and performed. From the much-maligned Rob Kiernan at centre half to the industrious Andy Halliday in midfield to the evergreen Kenny Miller up front, they all, to a man, contributed.

The substitutions highlighted the gulf that, off the field at least, exists between these teams just now. Celtic brought on Callum McGregor, Sviatchenko, a Danish internationalist and Rogic, who plays for Australia. Stuart Armstrong, Kris Commons and Colin Kazim-Richards remained on the bench.

Rangers, meanwhile, could only call on Nicky Clark, Nicky Law and Gedion Zelalem. No matter. They dominated their top flight opponents, in the first half in particular, and were worthy winners.

Celtic fans had many valid questions as they trudged dejectedly out of the stadium as their counterparts rejoiced. What does Kris Commons have to do to get a game? He is an experienced individual with a proven big game pedigree. So why did he remain on the bench?

Once again, Deila put his faith in Stefan Johansen, who failed to make a significant impact, behind lone striker Leigh Griffiths. That has frequently been the case this season. That reliance on his countryman has contributed greatly to his downfall.

Rogic should have featured from kick-off. He looked capable to engineering an opening or scoring himself after taking to the field and took his goal, after some impressive play and a clever cut back by Kieran Tierney, well.

Elsewhere, what was Dedryck Boyata doing in the starting line-up? The Belgian centre half had missed training at Lennoxtown last week and struggled from the first whistle. His side fared far better when he was replaced by Sviatchenko.

Why, too, did an experienced and Scott Brown and Nir Bitton toil? They had no answer to the slick passing, constant movement and high work rate of Dominic Ball, Halliday and Jason Holt in the middle of the park.

The 4-2-3-1 formation which Deila, with the rare exception, fields also irked many Celtic fans. It was hard to see yesterday what the benefits of it were once again yesterday.

Miller, at the grand old age of 36, opened the scoring for Rangers in the 16th minute after Brown diverted a Halliday pass into his path in the Celtic penalty area. His perfectly-executed first time shot beat Craig Gordon and found the bottom left corner.

Rangers bossed play thereafter and were unfortunate not to build on that lead. But Celtic drew level after making a rousing start to the second half. Sviatchenko rose well and headed home a Roberts corner in the 50th minute.

That led to a tentative end to regulation time which came to an end when Griffiths had a long-range free-kick pushed onto the crossbar by Wes Foderingham.

McKay, who was exceptional throughout the game and the rightful recipient of the Man of the Match award, capped his outstanding individual display with a drive from 20 yards out five minutes into extra-time.

Rogic took the game between the fierce city rivals to penalties for the first time in a major competition. In a cruel finish to an excellent game, he was the man who scooped his spot kick over the crossbar.

It all whetted the appetite for four Old Firm games next season. Ronny Deila, though, will not be around for them.