Celta knocked out La Liga's Villarreal 2-1 on aggregate after winning a 91st-minute penalty to snatch a 1-0 second-leg victory away at the Madrigal.
"It's a great satisfaction for me to see the way the youngsters are celebrating in the dressing room. That's the best prize," Sacristan told reporters after the game.
"It's also a great prize for the Celta fans after these difficult years. Now they have something to celebrate."
Celta were top-flight regulars during the nineties and at the beginning of the last decade, also playing in the UEFA Cup regularly and in the Champions League in the 2003-4 season.
Relegation in 2007, however, helped tip the club into an economic crisis and sucked them into relegation battles in each of their last two seasons in the second division.
Former-Celta player Sacristan, Frank Rijkaard's right-hand man at Barcelona for five years, arrived as coach towards the end of last season but they are still only 14th in the standings.
Their assured performances over both legs of their last-16 Cup tie should be a confidence boost for a young side that boasts a number of players promoted from the youth system.
Unlike other European competition contenders, Villarreal's poor start to the La Liga season, they are 10th, meant they had had high hopes of progressing in the Cup and played near full-strength sides.
Celta could meet a second division rival Recreativo Huelva in the quarter-finals next week, as the Andalucians hold a 3-0 first-leg advantage over Atletico Madrid. The second leg is at the Calderon on Thursday.
