Michael Beale, Brendan Rodgers react after Celtic claim controversial win over Rangers

After Rabbi Matondo had an offside goal disallowed in the opening minute, the Gers thought they has made the breakthrough on the half-hour mark when Kemar Roofe fired past Joe Hart after receiving a pass inside the area from Cyriel Dessers.

However, the goal was chalked off by referee Don Robertson following an on-field VAR review, after Dessers was controversially deemed to have fouled Gustaf Lagerbielke in the build-up, even though the Celtic centre-back appeared to kick the heels of the Rangers striker while being dispossessed.

Three minutes before half time, Celtic opened the scoring courtesy of a sweetly-struck volley from outside the penalty area by Kyogo Furuhashi that silenced the frustrated home crowd.

Rangers pushed for an equaliser after the break and they came close through chances from Sam Lammers and Danilo, but a cacophony of boos reverberated around Ibrox as Celtic held on for maximum points to climb to the top of the Scottish Premiership table.

After suffering a heavy 5-1 loss in midweek to PSV Eindhoven in Champions League qualifying, the pressure is beginning to mount on Rangers boss Beale, who expressed his disappointment after their latest setback against Celtic.

"It's been a rough week. Today, I thought the performance merited more in the game," Beale told BBC Scotland. "I thought we started the game quite well - obviously we score an offside goal, and then the VAR call. Having seen it back, he kicks Cyriel, so I think it's a harsh call. I think that's one that's gone against us, but there's a lot of time to play in the game.

"The goal is an error on our part, a huge error, and second half, we pushed and pushed, but you'd like us to be more inventive and ruthless, because the chances were there. It's a desperately disappointing day for everybody. We're behind them, and we have a lot of catching up to do. I thought we were strong in the game.

"There's areas we can improve on, but we had the moments - we were in front of Joe Hart two or three times and our last pass or shot wasn't good enough. That's where the frustration is. We have to come back stronger after the international break."

Beale added: "I completely understand [the fans' booing at full time]. We want the expectations to be high. The fans today stuck by their team for a long time, and it's natural that if you don't get a result in the derby that fans show their frustration.

"We have to dust ourselves down and come back. We have to go on a run. There's 34 games to go. The most important thing is focusing on getting this group consistently playing to a stronger level than it is right now.

"We went with a really bold, attacking team, and that was then added to by the boys that come off the sides. We had a right go, we chased the game, we had more moments than Celtic, and we didn't take them."

Meanwhile, Celtic manager Brendan Rodgers hailed the "massive result" secured by his side considering "virtually half the team" was absent due to injury.

"I said to them before the game that I need my men today. You need to come here, with 50,000 baying for blood, you need to come and play like a man, even though you're really young players," said the Northern Irishman.

"We had chances to score before we did, but we forced one or two passes. It's a great finish from Kyogo, and it puts us in a position that I thought we deserved at half time. The players stood up. The two centre-halves - Liam Scales was outstanding today. It's a fantastic win for us.

"A lot of the new players needed that big win to feel what the intensity is like at a club like Celtic. Second half, we had to show resilience and fight. To come here, keep a clean sheet, and win with not one supporter in the stadium is a brilliant win."

Discussing Rangers' disallowed goal, Rodgers added: "We had controlled the game up until that point, so I would have been disappointed. Obviously Gustaf [Lagerbielke] has to be quicker getting his passes away, but it looks like he's just been nicked from behind.

"Rangers will probably say it was never a foul, but there's enough officials looking at it, and they obviously deemed it to be a foul.

"It's still very early in the season. You don't win anything in September. We've just got to stay calm. This is a very young group that's missing some influential players at the moment. Once we get them back, they're only going to get better. In spells we've looked good, but it's nowhere near where I want us to be."

Rangers are next in action after the international break when they travel to St Johnstone in the Premiership on September 16, while Celtic play host to Dundee in their next match at Parkhead on the same day.