Former Three Lions internationals such as Gary Lineker and Rio Ferdinand have blasted Roy Hodgson's side on the micro-blogging site, particularly after their uninspiring 1-1 draw against Ireland last week.
But the Manchester City shot-stopper brushed off those comments saying he simply ignores it, and is adamant that the squad are only thinking about preparing for their upcoming World Cup qualifiers.
"We're not interested in stuff like that. They can tweet all they want from their sofas - we are out here doing it," the England goalkeeper said when asked about the Twitter critics.
"It is hard work and we are enjoying it. No-one in the squad is interested and they can tweet all they want."
The 26-year-old was one of England's star performers as they recorded an impressive 2-2 draw against Brazil at the Maracana Stadium on Sunday. A succession of first half saves kept the visitors in the game before goals from Alex Oxlade-Chamberlain and Wayne Rooney almost secured a famous win.
"It was pretty relentless in the first half, but we did what we usually do when our backs are against the wall - we fight until the end and never give in," the Man City goalkeeper continued.
"The Ox came on and did what he did. I would like to think English footballers fight until the end, particularly for all the fans who came out here. We got a result, and it's right up there with the best I have achieved."
England will have two games in hand by the time they face Moldova and Ukraine in September, but by then they could be five points behind Group H leaders Montenegro if the Balkan country beat Ukraine on Friday.
"I would love to be back in Brazil next year but we have a long hard road ahead of us and we will put everything we can into it," Hart added.