England manager Southgate was criticised by many, including Neville, for not bringing on midfielder Phil Foden during Friday's goalless World Cup draw with the United States.
Speaking in his role as a pundit for ITV, Neville – capped 85 times by England – said: "Phil Foden is a generational talent that I feel as though he has to play.
"He has to be played into form, and it has to work with England. I went through my career with England where there were times Paul Scholes was mishandled.
"I even woke up this morning thinking, 'has something happened in training? Has something happened off the pitch which has meant Gareth hasn't seen what he wants to see?'."
However, Grealish denies Southgate has any issues with individuals, having himself been in a similar position to Foden at Euro 2020 when struggling for minutes.
"If he did have a problem they'd know about it," he told BBC Sport. "I saw something, it might have been Gary Neville saying there's something going on behind the scenes.
"People always used to say 'he's got a problem with Jack' last year or two years ago and then I come on and it's like, 'he likes Jack now, who's it next?'.
"Then it's that he doesn't like Madders [James Maddison] and now he's in. Phil didn't play so he might have a problem with him. He doesn't have a problem with anyone.
"He speaks to all of us the same. Phil didn't play the other night but he's still the same with Phil as he is with me or Harry Kane – he's not got a problem with anyone."
England beat Iran 6-2 to make their best start to a World Cup campaign before underwhelming in their stalemate with the USA.
With four points from two matches, Southgate's side will advance to the last 16 if they avoid a four-goal defeat to Wales at Ahmed bin Ali Stadium on Tuesday.
That has not stopped Southgate being criticised for his team selection, but Grealish added: "Sometimes I just think whatever happens with England there's always something.
"We scored six and we were the best thing since sliced bread and then we didn't score for 90 minutes and it's the end of the world. We're top of the group, it's in our hands."