Lineker took to Twitter last week to accuse Roy Hodgson of leading the team back into the Dark Ages as they laboured to an uninspiring 1-1 draw against the Republic of Ireland at Wembley.
"They can tweet all they want from their sofas," said Hart. "We are out here doing it. It is hard work and we are enjoying it. No-one in the squad is interested and they can tweet all they want.
"England footballers fight to the end and never give in, especially for all the fans who came out to Brazil. We got a result and I would love to be back next year, but it's a long hard road ahead."