Southgate did not appear to have a good relationship with Arsenal defender Ben White.
The center-half and right-back went back home at the 2022 World Cup in Qatar, and has never played for England since.
Speaking to talkSPORT, former England striker Darren Bent felt Southgate lied when he said “nothing happened” behind the scenes with White.
"I'm pretty sure he always wanted to play for England but had a problem with Gareth Southgate and Steve Holland," said Bent.
"Some fans might not see it and they’ll say: 'Just get on with it, you’re playing for England'. But you have to be comfortable within a working environment.
"As soon as they've gone, if he's saying that he wants to be selected for England, that tells me that it's never been about playing for his country.
"I’m sure if you sat him down and asked him, he’d say representing his country is the highest honour you can get, but the fact that Southgate came out and lied basically, saying that nothing happened, be honest.
"Say that: 'We've had a bit of a falling-out and he's opted not to come back'. Then it would be fair enough, but he's almost tried to put it on Ben White and said 'blame him, not me' and that's not really fair in my eyes.
"He's done a lot of good for England in uniting the players, the press and the fans but just be honest about it, don't put it all on Ben."
- Get breaking football news faster with the new Tribal Football app! Download now on iOS and Android to stay ahead of all the latest transfers and football updates. Download now: App Store, Google Play