England will now face
But Arsenal winger Walcott would not have been fazed by the prospect of meeting tournament favourite
He said: "Did we want to avoid
"Playing the world champions, the European champions, is always going to be difficult but we will take anyone at this moment in time.
"The Italians will be tough but we've got some great players in that dressing room and I think we can go far.
"I feel we believe we could beat anyone the way we are playing as well.
"If we play to the best of our ability, who knows what can happen? Anything can happen. We defend well, we always know we can score goals so, if we keep clean sheets, we will definitely win."
Walcott believes it is important for England to recharge its batteries before focusing on trying to topple the Italians who finished runners-up in their group to
He said: "We haven't seen too much of them yet. They have world class players, also players who can come off the bench and make a difference as well.
"But I think it's good for the lads not to worry about that now.
"I think we need to relax, mentally have a break, and the extra day by playing on Sunday is going to help everyone.
"Our target is to take it game by game and it's working so far. Everyone is doing their jobs right and trust each other which is important.
"Can we win it? We are not going to think like that. We've got a great chance but seven other teams have as well."
He said: ""It doesn't matter who the quarter-final opponents are. The main thing was to get through the group and to finish top
"We know our qualities and what we're capable of. We've worked hard and done a lot of tactical play in training.
"We're difficult to beat and I don't think any team will fancy playing us."
England manager Roy Hodgson is frustrated that Chelsea, Manchester City and Tottenham Hotspur have planned exhibition matches overseas as soon as the EPL season is done.