Liverpool coach Rafa Benitez slammed his side for a shambolic showing after they compromised their hopes of advancing to the knockout stage of the Champions League with a 2-0 loss on Tuesday at Group E rivals Fiorentina.
The five-time European champions had done the minimum in seeing off Hungary's Debrecen to open their campaign at Anfield but the English Premiership giants were undone by two first-half goals from teen Montenegrin striker Stevan Jovetic.
With French side Lyon crushing Debrecen 4-0 away they now lead the group and can travel to Anfield for their next game full of confidence.
Benitez said Liverpool had to pull their socks up if they wanted to advance.
"If you want to win you have to score. We were not the best in any part of the pitch. We were giving the ball away all the time," he told Sky Sports.
Arsenal gave the English contingent some cheer with a 2-0 home win over Olympiakos of Greece with Robin Van Persie and Andrei Arshavin on the mark after the break as coach Arsene Wenger vowed to wrap up passage to the last 16 "as quickly as possible."
Group H rivals AZ Alkmaar and Standard Liege, whom the pool-topping Gunners have already seen off away, parted 1-1.
But Scottish fans suffered a horror show as Rangers, having started with a gutsy draw at Germany's Stuttgart, went down 4-1 at home to a rampant Sevilla of Spain in Group G.
Stuttgart again drew, this time at Romania's Unirea Urziceni, who held them 1-1.
In stark contrast to woeful Liverpool, Lyon were on fire in Budapest.
Kim Kallstrom scored after just three minutes, firing home a half volley home following a Miralem Pjanic corner from the left and the French doubled their lead when Pjanic netted a freekick after 13 minutes.
Lyon were running riot and Sidney Govou headed in a third on 24 minutes after another Pjanic corner kick routine caused havoc in the home backline.
Bafetimbi Gomis lobbed home the fourth after the break.
"I think we made the game look easy," concluded Lyon coach Claude Puel.
Liverpool preferred to make things hard for themselves as Fiorentina stepped through the gears to bounce back from their loss at Lyon.
And the Italians earned swift reward when Montenegrin striker Jovetic, only starting in the absence of the suspended Alberto Gilardino, stunned the visitors with two goals inside nine minutes on his competition debut.
Cristiano Zanetti picked him out with a neat through ball and Jovetic, who netted Saturday's winner in Serie A at Livorno, slipped the ball expertly past keeper Pepe Reina after 28 minutes.
The 19-year-old then struck again on 37 minutes, nudging home instinctively as Juan Vargas fed him from out on the left flank.
Lucas Leiva headed millimetres over as Liverpool tried to rally after the interval but they never looked capable of a comeback of the kind they produced to come back from three goals down in the 2005 final in beating AC Milan on spotkicks.
Holders Barcelona, having held Group F rivals Inter Milan in Italy in their first game, swatted Dynamo Kiev with Lionel Messi bagging the opener and Pedro Rodriguez hitting the clincher.
"That's a really important win for us - it's crucial to win your home matches," said Pedro afterwards.
In the same group Jose Mourinho's Inter could only manage a 1-1 draw at Russian newcomers Kazan, who had the temerity to take an early lead courtesy of Argentine striker Alejandro Dominguez's meaty drive.
Inter levelled after 25 minutes, with the unmarked Dejan Stankovic heading in but were grateful to survive the final half hour with 10 men for a point after striker Mario Balotelli was dismissed for a second bookable offence.
Mourinho's men are now third in the table two points behind Barca and one adrift of Kiev.