It will be the Potters' third consecutive season in the top-flight.
"It is difficult, but every game in this league is," former Manchester United youngster Shawcross told the club's website. "Obviously the Spurs match will be fantastic because it will be our first game here, and we will want to put on a great show for the supporters.
"You look at our first four or five games and there are some big teams there, but we can't be afraid. We have been here for two years now, so we will be in a better position to deal with these sort of occasions, and hopefully we will show that out on the pitch.
"Obviously, we will still be underdogs, but in football anything can happen, and we will be going in to these games with confidence after another superb season last year."