Grealish was not among the penalty takers as the Three Lions’ bid for only their second major tournament triumph ended in agonising failure at Wembley on Sunday night.
Marcus Rashford, Jadon Sancho and Bukayo Saka all failed from the spot as Italy clinched a 3-2 shoot-out win.
That drew criticism from former Manchester United midfielder Roy Keane, who criticised Grealish and Raheem Sterling for not stepping up, particularly ahead of 19-year-old Saka, who had never taken a penalty before.
But responding to Keane on social media, a fuming Grealish insisted he had put his name forward, only for England boss Gareth Southgate to opt for other takers.
Grealish posted on Twitter: “I said I wanted to take one!!!!
“The gaffer has made so many right decisions through this tournament and he did tonight!
“But I won’t have people say that I didn’t want to take a peno when I said I will.”
Speaking on ITV after the match, Keane said: "If you're (Raheem) Sterling or (Jack) Grealish, you cannot sit there and have a young kid [Saka] go up for a penalty ahead of you, you can't.
“You cannot let a shy 19-year-old go up in front of you. They have a lot more experience, Sterling has won trophies, they had to get in front of the young kid and stand up."
Southgate, speaking on Monday, reiterated he alone had been responsible for choosing England’s penalty takers.
“It is my decision who takes the penalties,” he said. “It is not a case of players not volunteering or more experienced players backing out.
“They didn;t have the chance. It was my decision, nobody else's. It was my decision to give those players the penalties they took.”