Gareth Southgate should leave his role as England manager "with his head held high" after the World Cup, according to Jamie Carragher, who says the Three Lions have overachieved during his reign.

Southgate has led England to at least the semi-finals in consecutive major tournaments, becoming the only boss to do so since Alf Ramsey (World Cup winners in 1966, Euro 1968 semi-finalists). 

However, he has faced heavy criticism since he oversaw England's relegation from the top tier of the Nations League in September, and was jeered by supporters following a defeat in Italy.  

While Southgate signed a contract extension to run until the end of Euro 2024 last year, Carragher believes he should call time on his tenure after the trip to Qatar, but says he has earnt the right to make his own decision.

"If I was Gareth Southgate, I would make the Qatar World Cup my swansong as England manager," Carragher wrote in the Telegraph. "Hopefully England will produce to a strong enough level to ensure that is Southgate's call.

"After his excellence in the job to this point, the least he deserves is to leave on his own terms when he feels the time is right. 

"The natural cycle should be for a rethink every four years, so a coach builds towards the next World Cup. Unless Southgate has the energy for that, it is wiser to step away.

"Southgate may win over the doubters for a third time over the next few weeks. My hope for Qatar is for England to again retain interest in the competition until the final week, to give Southgate the option of leaving the job through the front door with his head held high."

Southgate has been charged with adopting a negative approach in several big games during his reign – notably 2018's World Cup semi-final defeat to Croatia and the Euro 2020 final loss to Italy.

However, Carragher described criticism of his tactics as a "joke" as he insisted England had not underperformed in recent years.

"He is intelligent enough to have sensed a mood shift over the last few months, even if some of the negativity surrounding him during the build-up to the tournament is a joke," Carragher added.

"It is unreasonable to suggest he should change course from the formula that took England so far in their last two competitions.

"He has not failed to get the most of a talented squad, as some argue. He has over performed with a very good bunch.

"Go through the current England team and there are three players who would be a regular first choice in any club side in the world – Harry Kane, Phil Foden and, in the future, Jude Bellingham.

"The suggestion that this is the greatest England team since 1966 is a myth, but the more it gains traction, the more Southgate must deal with unrealistic demands."