The Villa skipper set up Raheem Sterling for the only goal of the game as England beat the Czech Republic on Tuesday to top Group D and move into the last-16 with an unbeaten record.
Grealish is now hungry for more as he looks to match the impact made by Gascoigne at the 1990 World Cup and Rooney in Euro 2004.
Both lit up those tournaments after breaking into the England team and Grealish has the same ambition to announce himself on the world stage.
He said: “I have spoken about how big these tournaments can be in players' careers.
"If you look back and think of Gazza at Italia 90, he was obviously still well known before, but I think everyone remembers him for that tournament especially.
"You look at Wayne Rooney in Euro 2004 - I think that was where he set his marker to say I am going to be one of the best in the world.
"I am hoping to follow in their footsteps and hopefully I can do that if I get more chances in this tournament."
Grealish’s first start at a major tournament followed a public clamour for his inclusion, after the Villa ace was limited to just one substitute appearance in England’s first two group games.
But the 25-year-old insisted the extra attention did not affect his approach. Instead, he rather relished it.
"I don't think it is pressure," said Grealish. "I love playing football. That is what I am paid to do. That is what I have been born to do.
"I just play football every day of my life. When I go out there and play it is no pressure on me whatsoever. I go out there and just enjoy myself like I always do.
"I felt like I had a good performance but I still maybe felt like in the second half I could have got on the ball a little more and probably tried to dictate the game a little more.
"I have never played in the Europa League or Champions League before, so it is obviously different to what I am used to," he added.
"I love it and if I perform on this stage it is a matter of showcasing my talent to the world and that is what I want to do."
Tuesday's win saw England complete the group stage of a major tournament without conceding a goal for only the third time in history, after previously beating Croatia 1-0 and drawing 0-0 with Scotland.
Yet while Southgate's team have also been criticised for a lack of attacking fluency, Grealish is confident there is more to come.
He said: "It's a brilliant achievement topping a group without conceding and it shows that everything we've been working on in training field has paid off.
"Attacking-wise we can still step it up. We've got so much talent. I heard the manager say that in one of his interviews and he's bang on
"But, I know we can score more goals. I wouldn't mind my first goal for my country to be honest, I don't know when that's going to come to be honest. I think I'm nine games in now so hopefully that'll come but, as a team, I'm happy assisting at the moment."