The League One side beat Championship club Charlton in the last round.
"We'll be going into every game to win, but we've got to be realistic as well," Wright told BBC Essex.
"Both sides are flying at the top of the Premier League, they're aiming for the top four and maybe even the title."
Fourth-placed Spurs and second-placed Leicester drew 2-2 at White Hart Lane on Sunday, and the winners of the replay will travel to Colchester at the end of this month.
"We need to make sure we don't get overawed by the occasion and give a real good account of ourselves, because it is the FA Cup and you never know," added Wright, who became the club's assistant manager when Kevin Keen was appointed as U's boss last month.
"They'll be coming to our place and the pressure will be all on either team that gets through.
"We can set ourselves up and really enjoy the occasion and hopefully cause them a number of problems."
Colchester United assistant manager David Wright says the club must be realistic about their chances of overcoming Tottenham or Leicester City in the fourth round of the FA Cup.