The Gunners were comprehensively outplayed at Anfield on Sunday afternoon as goals from Roberto Firmino, Sadio Mane, Mohamed Salah and Daniel Sturridge clinched an emphatic victory.
The result will do little to dampen speculation over the future of a number of Arsenal players, with the summer transfer window closing on Thursday night.
Oxlade-Chamberlain has rejected a new contract at the Emirates and is said to be pushing for a move with Chelsea and Liverpool interested in securing a deal.
Sanchez, meanwhile, has been strongly linked with a summer departure for many months – Manchester City, Bayern Munich and Paris Saint-Germain are among the clubs monitoring his situation.
Thierry Henry questioned whether the duo should stay at Arsenal following another capitulation against a title rival and Carragher was quick to interrupt the French legend.
‘They shouldn’t be staying,’ he told Sky Sports.
‘In the last 10 years it’s always been the same movie. From the top to the bottom, there’s a lack of ruthlessness at the club.’
Carragher also expressed the belief that Wenger, who signed a two-year contract extension over the summer, should have been sacked by Arsenal.
‘If we’re being honest, the board bottled the decision. They’re terrified of moving the manager on. But that had to be the decision,’ he said.
‘Last season I called them cowards and I’ll say it again. That was even worse than Crystal Palace last year.
‘Nothing will change over the next two years.’
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On Sanchez’s future in north London, Henry added: ‘Those guys are going away on international duty now so we will see what happens.
‘If you’re Sanchez, he didn’t look like he wanted to stay [today].’