Leicester have work to do after being held 1-1 at home by Spartak Moscow.
Bayer Leverkusen were also winners in Group G as the Germans came from behind to beat Ferencvaros 2-1 thanks to a second-half winner from 18-year-old star Florian Wirtz.
The Foxes narrowly missed out on qualification for the Champions League last season, finishing fifth in the Premier League but winning the FA Cup.
Celtic must now recover in time for this weekend's start of the Scottish Premiership season. They face Hearts on Saturday.
The 55-year-old Australian signed a 12-month rolling contract and fills the vacancy on a permanent basis left open when Neil Lennon resigned in late February.
Fans ignored pleas from the club and government to disperse as they then marched from Ibrox into Glasgow city centre.
Having ended Celtic’s bid for a 10th successive Scottish title, Rangers finished with 102 points after going unbeaten through the entire 38-game campaign.
Scottish Premiership: Former Bournemouth boss Eddie Howe favoured to replace Neil Lennon as Celtic manager
Eddie Howe has held discussions with members of the club's board, including major shareholder Irish financier Dermot Desmond.
"It is very difficult to put into words right now," Gerrard told the club's website after leading Rangers to their first league title in a decade. "I'm on a real, emotional high and it has been a journey that is not finished."
Scottish Premiership: Undefeated Rangers claim first title in 10 years ending Celtic's stranglehold on league
Over the past decade, Rangers were not even in the top-flight for four seasons after the club was demoted to the fourth tier after being liquidated in 2012 due to financial troubles. "This club has been to hell and back over the past 10 years," said manager Steven Gerrard.
A list of exemptions published by the UK government allowed "elite sportspeople (and their coaches if necessary, or parents/guardians if they are under 18) - or those on an official elite sports pathway - to compete and train".
Europa League: Tottenham salvage point against LASK Linz to reach knockout stage; AC Milan, Rangers also advance
In Linz, the hosts dominated the first half but only scored once, through Peter Michorl. Spurs, who had not managed a shot on target, won a penalty for handball in added time. Gareth Bale converted for his 200th career goal.
Europa League: 'Loved and appreciated' Gareth Bale starts as Tottenham Hotspur win, Celtic undone by AC Milan
After coming on as a substitute against West Ham for his first appearance since returning to Tottenham, Bale played more than an hour against in the Group J match against Austria's LASK, and had a hand in Tottenham's second goal.
Europa League Draw: Seven-time European champions AC Milan placed in group with Celtic, Sparta Prague, Lille
AC Milan, which last won the Champions League in 2007, came from the pot of third-seeded teams. Scottish champion Celtic was the top-seeded team.
Europa League: Tottenham literally move the goalposts to win in Macedonia, AC Milan survive without Zlatan Ibrahimovic
Son Heung-min and Harry Kane struck in the final 20 minutes to set up a playoff round tie at home to Maccabi Haifa next Thursday on an eventful night in Macedonia for Jose Mourinho's men.
The 49-year-old Celtic manager was also left counting the financial cost for the club of their second qualifying round exit, the first time in 15 years they have gone out so early.
Coronavirus Outbreak: Scottish Premiership games involving Celtic and Aberdeen postponed following player rule breaches
Football authorities and government officials held a meeting after Celtic defender Boli Bolingoli took a secret trip to Spain, failed to self-isolate on his return, and played in a 1-1 draw with Kilmarnock in the league on Sunday.
Coronavirus Outbreak: Scottish Premiership under threat after Celtic's Boli Bolingoli breaks quarantine rules
Celtic's Belgian defender Boli Bolingoli said he had not observed quarantine protocols after a trip to Spain. Anyone returning to Scotland from Spain must spend two weeks in quarantine.
Celtic fully deserved to be crowned Scottish Premiership winners for their consistency during a season cut short by the COVID-19 crisis, manager Neil Lennon has said.
Coronavirus Outbreak: Celtic named champions, Hearts relegated as Scottish season ends due to pandemic
Celtic have been named champions of Scotland after the clubs voted on Monday to end the season early due to the COVID-19 pandemic, the Scottish Professional Football League said in a statement.