England's campaign in Qatar came to a heart-breaking end in the quarter-finals as they suffered a 2-1 defeat against the reigning world champions on Saturday night despite producing an impressive performance.
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It was a disappointing end to a tournament that promised so much for the Three Lions, who looked very impressive during wins over Iran, Wales and Senegal.
Southgate has a contract until Euro 2024 but admits he is now weighing up whether to stay on or step aside having faced plenty of criticism in recent years.
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"When I've been through the past few tournaments my emotions have been difficult to really think through properly in those following few weeks," Southgate said.
"It took so much energy out of you and you have so much going through your mind.
"I want to make the right decision either way because it has to be the right one to go again, or the right one not to go again and I don't think tonight is the time to make a decision like that.
"I've found large parts of the last 18 months difficult.
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"For everything that I've loved about the last few weeks, I still have how things have been for 18 months - what's been said and what's been written, the night at Wolves.
"There are lots of things in my head that are really conflicted at the moment, so what I want to make sure, if it's the right thing to stay, is that I've definitely got the energy to do that."
Pearce, who played alongside Southgate for England, is hopeful his former teammate will carry on in his post.
And the talkSPORT pundit also revealed what he said in a text to the manager following the defeat to France.
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"I've dropped him a text this morning just saying how proud I am of him and the squad," Pearce told talkSPORT on Sunday.
"I hope he stays in post and drives this team forward because I'm so proud of them and have been in the previous tournament as well and prior to that in Russia.
"I'm so proud of all the players for what they're achieving and also what they stand for and the togetherness and pride in the shirt as an ex-England player.
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"I hope that he carries on in his role because he's the one whose knitted this all together and it would worry me if he were to step away.
"He'll think things out, he's very studied in what he does. I hope fingers crossed that he stays in post."
Gary Neville and Alan Shearer are among other ex-England stars who insists Southgate should stay in post, having led England to a quarter-final and semi-final of a World Cup and a European Championship final.
Neville posted on Twitter: "I hope and want GS to continue to 2024.
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"Having just read his quotes it seems he's seriously considering whether to carry on.
"I suspect he's torn between the feeling of leaving now with great respect and intact v a potential sour ending in the future. One he's seen so many times."
Shearer, meanwhile, said to BBC Sport: "I have no doubt at all that Gareth Southgate should stay on as England manager to take us to the 2024 European Championship.
"I know he hasn't delivered the trophy we wanted in Qatar, but we have to look at the bigger picture. Not only about how we have played at this tournament but also the progress we have made during his six years in charge."
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While England legends want Southgate to stay, the 52-year-old has attracted criticism during his time as England manager despite impressive performances at major tournaments.
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Journalist Darren Lewis has also been keen to stress where England were when Southgate first took charge six years ago and what he's brought to the team since.
"After Iceland in Euro 2016 you couldn't see where they were going. We were a team, we had tactics but there wasn't an affinity between the team and the nation," Lewis told talkSPORT.
"You couldn't really see us playing decent football that made you proud of the country and you couldn't really see where we went from there.
"But with this team you can see there are young players that are going to form the nucleus of the side going into Euro 2024.
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"You can see there's a culture within the squad that Gareth has put together, or harmony, of unity. There is a consistency of tactics and team selection, there is a boldness.
"You can see that he's evolved the team. From five at the back to get us through to the final of the Euros to four at the back in which we expressed ourselves against the defending champions."
Meanwhile, Andy Townsend believes other managers can learn from Southgate.
"There are a lot of people who have been very impressed by what Gareth's done, the way he's gone about it and I'm certainly one of those," Townsend added.
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"I think a lot of very experienced managers could learn an awful lot from him. The way he handles himself, the way he speaks, the way he has forged very strong bonds and relationships with his players."