The only side from outside the top flight left in the last eight, Celta have a decent chance of advancing to the last four when they host Atletico Madrid on Thursday after they earned a 1-1 draw in Madrid in last week's quarter-final first-leg.
"It's been a competition in which we have felt very much at home from the start," Sacristan said in an interview with the Faro de Vigo newspaper published on Tuesday.
"Perhaps our younger players haven't felt the pressure you are under in the league to win the three points," he added.
"It has created a really strong sense of excitement being able to get through the ties and beat first-division sides and has helped us grow as a team."
Celta, relegated to the second division at the end of the 2006/07 season and currently in 17th spot out of 22, have never won the Cup, having lost three times in the final, while Atletico last triumphed in 1996.
"You have to bear in mind that we are facing one of the best teams in the Spanish league, with players of enormous potential," Sacristan said.
"They remain the favourites, despite the fact that we played a very good match in Madrid. If we let our level drop for a moment the quality of the Atletico players will be decisive."
Sevilla, the 2007 winners and conquerors of holders Barcelona in the last round, have one foot in the semi-finals after they win 3-0 at Depor in the first leg and host the Galicians on Wednesday.
In other all-La Liga second-legs, Getafe host Real Mallorca on Thursday with a 2-1 lead from the first leg and Racing Santander travel to Osasuna on Wednesday after winning 2-1 at home last week.
In the semi-finals, in the first two weeks of February, Sevilla or Depor would play Getafe or Mallorca and Celta or Atletico are set to meet Racing or Osasuna.
