But after the break the visitors roused themselves, and goals from Vinicius Junior, Luka Modric and Eden Hazard showed their class and secured victory.

Carlo Ancelotti's side - who lost Karim Benzema to injury in the first half - join Shakhtar Donetsk at the top of Group F after they defeated RB Leipzig.

Celtic travel to Warsaw to face the Ukranian side next Wednesday in their second group game, aiming to get their campaign back on track, after their grand return against European football royalty ended in disappointment.

But it was not a dispiriting night at a bouncing Celtic Park as the Scottish champions made a good impression on the biggest stage.

Ange Postecoglou vowed his team would be true to their front-foot style despite Real's quality, and it was in evidence straight from kick-off as they pressed Thibaut Courtois into kicking the ball out after 12 seconds. From the throw-in, Liel Abada lashed just wide as the stadium roared its approval.

It was not a flash in the pan either, with the Israeli winger set free in behind the defence after a wonderful pass from Jota, but his rushed shot went straight into Courtois' hands.

And after McGregor rattled an upright from the edge of the area and half-time substitute Daizen Maeda scuffed a brilliant opportunity from six yards, there was a sense of foreboding that Celtic's missed chances would haunt them.

Almost inevitably the five-time European champions Modric and Tony Kroos grew in influence and Real did punish Celtic's profligacy in a beautifully effective four minutes.

A flowing move which started at the feet of Courtois ended with Vinicius planting Federico Valverde's cross in the bottom corner, before Hazard set up Modric to caress home at the second attempt.

With Celtic suffering from their first-half exertions, Real controlled the ball with greater ease and put together a stunning 33-pass move which culminated in Kroos picking out Dani Carvajal, who stroked across goal for Hazard to tap home their third.

Celtic kept fighting to the end and still looked a threat in flurries, but ultimately they were outclassed in the second-half by the 14-time kings of Europe, whose quality shone through.

Player of the match - Luka Modric

There is little else to say about the Croatian maestro. Modric turns 37 on Friday but shows no sign of slowing down. He ran the show in the second half.

Celtic show mettle before Modric show - analysis

With two minutes left on the clock, and at 3-0 down, the Celtic fans were singing the name of their manager over and over. It shows how revered Postecoglou is because of the style of football he has brought, and it was on full show in the first half.

The midfield trio of McGregor, Reo Hatate, and Matt O'Riley buzzed about, Giorgos Giakoumakis was relentless up front, while centre-backs Moritz Jenz and Cameron Carter-Vickers defended diligently.

Had Abada showed his usual ruthless streak, things might have been different. As it was, Kroos and Modric did what Kroos and Modric do, superbly supported by precocious Frenchman Aurelien Tchouameni.

Kroos completed 119 passes on his own and his sublime ball for the third goal encapsulated his ability, and Modric just glided across the Celtic Park turf, stroking in the second goal with the outside of his boot.

The last time the little Croatian was in Glasgow he took Scotland apart at Euro 2020, also slamming in a beautiful goal. He obviously loves playing here, and was a joy to watch once more even as he turns 37.

Celtic were chasing shadows slightly by the end, but they can take encouragement their style can cause problems against the best, with RB Leipzig and Shakhtar Donetsk to come.

What they said

Celtic manager Ange Postecoglou: "Obviously disappointed with the outcome. I thought the first goal was always going to be important and up until that point we were well in the game.

"If anything, we had the better chances and you need to capitalise on them - and we didn't."

Real Madrid coach Carlo Ancelotti: ""It was like two games, first half we suffered a bit with intensity, second half we had control.

"We were not surprised [with Celtic's start]. We knew they could start really fast. We were lucky because they hit the post. Second half, was much better. When we opened to scoring it was easier for us to control the ball."

Match stats

• Celtic have never won their opening game of a Champions League campaign, with this the 11th time they have failed to do so (D2 L9). Their last three have all been defeats by at least three goals - 0-7 v Barcelona in 2016-17, 0-5 v Paris Saint-Germain in 2017-18 and 0-3 v Real this season.
• Only one of the last 28 title-holders have lost their first match of the following season's competition (W17 D10), with Liverpool losing 2-0 at Napoli in 2019-20.
• Since the start of last season, Real have won 100% of their away games in the group stage (4/4) without conceding a single goal, and scoring 12 times themselves.
• There were 33 uninterrupted passes in the build-up to Hazard's goal; since 2003-04 (as far back as data is available), this is the most in the build-up to any of Real Madrid's 434 goals in the competition in this period.
• At 36 years and 362 days, Modric became the oldest player to score for Real in the European Cup/Champions League since Ferenc Puskas in September 1965 (38y 173d v Feyenoord).
• Vinicius Junior has been directly involved in 17 goals in his last 18 appearances across all competitions, scoring nine and providing eight assists.
• Modric made his 100th Champions League appearance for Real, becoming just the eighth player to reach this milestone for the club (joining Iker Casillas, Raul, Sergio Ramos, Karim Benzema, Roberto Carlos, Marcelo and Cristiano Ronaldo).

What's next?

Celtic are at home to Livingston on Saturday in the Scottish Premiership (15:00 BST), before facing Shakhtar in Warsaw on Wednesday (17:45). Madrid have Mallorca at the weekend before hosting Leipzig.