The Manchester City stopper, who is currently on loan at West Ham United, has seen his spot between the sticks called into question following a number of questionable displays over the past 16 months.
Hart was at fault in games against Wales and Iceland at Euro 2016 and conceded two goals from long-range free kicks against Scotland during the current World Cup 2018 qualifying campaign.
"I spoke to Joe a while back and I said to him that at the Euros last summer, the ball went into the back of the net against Iceland and he didn't get up and berate his back line," he told Sky Sports News. "I played in front of Peter Shilton and for 90 minutes, he would rip your head off for a clean sheet.
"Even when you were 5-0 up, he'd be at you all the time and I think Joe needs more nastiness in his game that says to his defenders 'you've got to get me a clean sheet and to do that, I'm going to get onto you a little bit more because I want to stay in this team'. [The criticism] comes with the scrutiny of playing for England.
"His form has dropped and it was poor in the European Championships, and he admits that. He's a very honest guy. The challenge is coming from Jack Butland and if he didn't have those injuries and was out of Stoke's team for a while, it might be a little bit closer at the moment in time. The emergence of Jordan Pickford and Tom Heaton as well means he's under a bit of pressure, but he's got to rise to that challenge."
Hart admitted earlier this week to being unhappy with the way he was overlooked for inclusion by Man City boss Pep Guardiola, having spent two seasons out on loan since the Catalan coach's arrival at the Etihad Stadium.