While they sit top of their Euros group, a poor draw with Denmark has raised questions about the realistic chances of England winning the Euros.
Rice said: "I think we are all so desperate to do the country proud. We are all so desperate to win, to be leaders, to go out there and give people memories for lifetimes.
"Sometimes I maybe feel like we put too much pressure on ourselves where we could just go out there and let it just take care of itself.
"I think there is probably more pressure now from the outside just because of the seasons some of our players have had.
"If you look at the goals that our front four have scored this year, it's over a hundred between them.
"Of course there is expectation because they are the best players in the world. And that goes for everyone throughout the team. There's going to be that pressure. This is England, major tournament.
"But look this is our job and this is what we have to deal with. At the end of the day it's us, we've played in high-pressure games, high-pressure environments."
