England ended a difficult week on a high as they emerged from the newly-reopened Maracana Stadium in Rio de Janeiro with a 2-2 draw that would have been a victory had it not been for a late equaliser from Paulinho.
Lineker had attacked Roy Hodgson on Twitter on Wednesday night, claiming the England boss had taken the national side "back to the dark ages" by playing a 4-4-2 system in the flat 1-1 draw against the Republic of Ireland.
Former England defender Rio Ferdinand joined in on the England-bashing the day after, claiming that the country needed a youth coaching overhaul after the national team had not played consistently well for a decade.
Bur Hart brushed off the comments, saying the squad were not interested in criticism from the likes of Lineker.
"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 comments such as Lineker's.
"It is hard work and we are enjoying it. No one in the squad is interested and they can tweet all they want."
Alex Oxlade-Chamberlain and Wayne Rooney both scored terrific goals on a memorable night at the stadium where John Barnes led England to one of their most famous victories 29 years ago.
But it was Hart who should take most credit from the game. He pulled off a series of top-class saves to fend off a Brazilian barrage in the first half, allowing England to come into the game in the second half.
Hart could do little to stop Fred scoring the opener and lax marking from Gary Cahill allowed Paulinho to grab an equaliser in the 82nd minute.
Hart saluted England's resolve, which he thinks bodes well for the future.
"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 Manchester City man added.
"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."
The encouraging result will count for nothing should England fail to make it back to Brazil next summer for the World Cup, however.
England will be five points behind Group H leaders Montenegro if the Balkan country beat Ukraine on Friday.
Hodgson's men will have two games in hand by the time they face Moldova and Ukraine in September, but they may have to win all four of their remaining games to qualify.
"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," said Hart, who won his 32nd cap last night.
"We have to take the positives though. We beat Spain and Brazil at home in friendlies.
"No one has taken us apart - we just need to get over the finish line (in qualifying).
"We dug in when we needed to and we have to repeat that (in September)."
Oxlade-Chamberlain's performance - which came 29 years after his father Mark had won 2-0 with England in the same stadium - was particularly pleasing for Hart.
"The Ox came on and scored a marvellous goal," the 26-year-old said.
"He is a great prospect at 19. He plays with freedom. The world is not against him and we have to protect him."