Giovanni van Bronckhorst says the gap in quality between Rangers and Liverpool was "obvious", though he vowed the Scottish Premiership side will learn from a comfortable defeat to the Reds.

Rangers have shipped nine goals in three Champions League games after a 2-0 defeat at Liverpool on Tuesday, which saw Van Bronckhorst's side remain bottom of Group A at the halfway point.

Trent Alexander-Arnold and Mohamed Salah struck in either half at Anfield as Rangers failed to find the net in their first three Champions League games for the first time ever.

While Rangers offered little in the way of challenging Alisson, barring a late chance for substitute Rabbi Matondo, Van Bronckhorst hopes his side will use the defeat as a lesson.

"The gap is obvious, we are competing against one of the best sides in Europe – it doesn't mean you have to lose the game," the Rangers manager told reporters.

"We competed well at times, set-pieces we defended really well. My team will learn from this game, I will learn, my players will and we will take this experience into the next game and also into the league.

"It was an experience we had again in the Champions League, it is a league we want to compete in but it is really, really hard against the teams we are facing now.

"It is experience, we did better than the first game but it is a level where you have to think quicker, pass quicker and move quicker.

"There were many moments where we won the ball but then we lost it, that is what we are facing at the moment and we need to improve in the next three games.

"The margin for error is very small against these great teams. It is everything you know, tactically, technically – first touches, movements, identifying movements when to speed up the games.

"We are doing so much better and my team will only improve. If that is enough to go through in Europe then we will take it."

A two-goal loss arguably flattered Rangers, who were thankful to the efforts of goalkeeper Allan McGregor after the veteran made eight saves during a fine individual performance.

"McGregor performed really well, he can perform on this level – especially the first half he had some good saves," Van Bronckhorst added.

"It was very positive to see his performance, also Leon King – an 18-year-old defender from the academy – and Ben Davies with his first 70 minutes of the season coming back to Liverpool he did well. There are always positives to take."

Rangers will look to make amends against Liverpool in the return fixture next Wednesday, with Van Bronckhorst's side trailing third-place Ajax by four points in a battle for Europa League qualification.

Liverpool made it back-to-back Champions League wins after a commanding 2-0 victory over Rangers, with Trent Alexander-Arnold scoring the pick of the goals.

Jurgen Klopp's side have been somewhat off the pace this season but soon took the lead at Anfield after an excellent Alexander-Arnold free-kick past Allan McGregor.

Mohamed Salah doubled the lead with a penalty after the interval, with the insipid Rangers thankful to McGregor for preventing Liverpool from inflicting further damage.

Victory kept the Reds a point behind Group A leaders Napoli, who thrashed Ajax in Tuesday's other game, while Rangers remain bottom after yet another disappointing showing in Europe - the Scottish side conceding nine goals in three group stage matches thus far.

McGregor denied a fizzing Darwin Nunez effort after just two minutes, but the Rangers goalkeeper had no chance five minutes later when Alexander-Arnold expertly curled a free-kick into the top-left corner.

Salah saw his whipped attempt tipped away by McGregor, who then produced two smart saves in quick succession against Nunez as Liverpool dominated the first half.

Salah coolly converted a 53rd-minute penalty down the middle after Leon King felled Luis Diaz, while McGregor continued his fine individual performance by parrying over Diogo Jota's ferocious shot minutes later.

Joel Matip headed narrowly wide from a glorious opportunity before Konstantinos Tsimikas cleared off the line after Rabbi Matondo slotted past Alisson in the closing stages, as Liverpool returned to winning ways after a 3-3 draw with Brighton and Hove Albion at the weekend.

What does it mean? Reds stay on the tails of Napoli

Despite a 4-1 humbling at the in-form Napoli on matchday one, Liverpool remain within touching distance of Luciano Spalletti's side at the halfway point in the Champions League group stage.

Ajax are just two points behind Jurgen Klopp's side, but the Reds will feel confident of another victory to bolster their knockout credentials when they return to Rangers next week.

By contrast, Rangers are without a win or a goal in their first three games in Europe this season – a stark difference from their victorious run to the Europa League final last season.

Awesome Alexander-Arnold

Much has been made of Alexander-Arnold's defensive capabilities, but the right-back quietened his critics with his inch-perfect opener; his sixth free-kick goal since the start of the 2016-17 season in all competitions.

No Liverpool player can match his tally in that period, while the strike made Alexander-Arnold the first Reds man to score from direct free-kick in the Champions League since Steven Gerrard against Basel in 2014.

Goal-shy Rangers' problems continue

Rangers have won just of eight European away games in England across all competitions, with that sole victory coming in a 2-1 triumph over Leeds United in 1992.

The Scottish giants may have been beaten Europa League finalists last term, but they failed to score once again here, marking the first time Rangers have not found the net in their opening three Champions League group games.

What's next?

Liverpool return to domestic action away at Premier League leaders Arsenal on Sunday, while Rangers host St. Mirren in the Scottish Premiership a day prior.

Allan McGregor stacked up the goalkeeping records as Rangers reached a European quarter-final for the first time since their run to the 2008 UEFA Cup final.

The 40-year-old made 11 saves to limit Red Star Belgrade to a 2-1 win in the second leg of their Europa League last-16 tie, giving Rangers a 4-2 aggregate victory.

That was three more saves than any other goalkeeper had managed in a Europa League game this season – Fernando Muslera of Galatasaray made eight against Marseille – and the most by a Rangers goalkeeper since the competition was launched in 2009-10, replacing the UEFA Cup.

McGregor's saves total was the highest ever by a goalkeeper aged 40 or above in the Europa League, Opta said. Only Tim Howard, who made 12 saves for Everton against Wolfsburg in 2014, has ever made more stops in a game for a British club in the competition.

Former Rangers boss Ally McCoist said of McGregor: "He's been fantastic over these two games.

"Some of these saves he's produced, you'd think he's 20 years of age again. He's been wonderful. What a servant to the football club."

It was the first time since David de Gea made 10 stops for Manchester United against Roma on May 6 last year that any goalkeeper had reached double figures in saves in a Europa League match.

McGregor was making his 50th appearance in the UEFA Cup/Europa League, becoming the first Rangers player to reach that landmark with the club.

The last player to make more saves in a Europa League game was Karl-Johan Johnsson of FC Copenhagen in their 1-0 quarter-final defeat to Manchester United in August 2020.

McGregor, who missed out on appearing in the 2008 UEFA Cup trophy match through injury, earned praise from current Rangers boss Giovanni van Bronckhorst.

"At moments he needs to be there, he is there. I'm really happy with his performances. Even at his age he's really important for us," Van Bronckhorst told BT Sport.

Rangers knocked out Borussia Dortmund in the first knockout round and are beginning to cut a swathe through a strong field of clubs, just as they did on their UEFA Cup run 14 years ago.

Mirko Ivanic gave Red Star an early lead on Thursday and they pushed for more, but Ryan Kent's goal against the run of play in the 56th minute put the Scottish visitors back in control.

A late penalty from El Fardou Ben Nabouhane gave Red Star victory on the night, but it was Rangers who were celebrating at the final whistle.

Van Bronckhorst added: "Our belief is only getting stronger. There are big teams left in the draw, so we have to wait and see tomorrow [when the draw takes place].

"The opponent will be stronger with each round. The result against Dortmund is one that the whole of Europe thinks is a great achievement. We're going to enjoy the night, and then prepare for Dundee on Sunday."

Rangers ended Old Firm rivals Celtic's Scottish Cup dominance and took a big stride towards completing the double with a 2-0 victory at Ibrox.

Steven Davis opened the scoring with an acrobatic strike and a first-half Jonjoe Kenny own goal put the Premiership champions well on course for the last eight.

There was no way back for the Hoops, who had lifted the trophy in the previous four seasons, and Allan McGregor saved Odsonne Edouard's penalty as they suffered a first defeat under caretaker boss John Kennedy.

Victory for Rangers ensured they have won three and drawn one of their four clashes against their fierce city rivals in what has been an outstanding season.

Davis gave Rangers the lead in style in the 10th minute, volleying in from close range when Joe Aribo's deflected shot looped up invitingly for the midfielder following a sharp turn and incisive run from Ryan Kent.

Edouard shot straight at Allan McGregor after creating space for himself in the Rangers penalty area, then Callum McGregor's drive deflected over the crossbar and Stephen Welsh somehow failed to finish as Celtic pressed for an equaliser.

Steven Gerrard's side doubled their lead 12 minutes before half-time, though, with Aribo conjuring up some trickery to beat Diego Laxalt before crossing from the right and Kenny turned into his own net attempting to prevent Kent from slotting home.

Celtic should have reduced the deficit when Mohamed Elyounoussi was superbly denied by Allan McGregor and Edouard volleyed wastefully over following up.

The Gers keeper did brilliantly to race off his line and thwart Elyounoussi soon after, the Celtic forward letting himself down with a poor first touch after Edouard set him up.

Allan McGregor then dived to his right to keep out Edouard's spot-kick 11 minutes from time after Aribo was adjudged to have fouled Leigh Griffiths, which summed up Celtic's afternoon.